@article{ADK2013,
  author = {Abramovich, Dan and Denef, Jan and Karu, Kalle},
  title = {\href{https://personal.math.ubc.ca/~karu/papers/weaktor.pdf}{Weak toroidalization over non-closed fields}},
  journal = {Manuscripta Mathematica},
  volume = {142}, number = {1-2}, year = {2013}, pages = {257--271},
  doi = {10.1007/s00229-013-0610-5},
  url = {https://personal.math.ubc.ca/~karu/papers/weaktor.pdf}
}

@article{AK2000,
  author = {Abramovich, Dan and Karu, Kalle},
  title = {\href{https://arxiv.org/abs/alg-geom/9707012v1}{Weak semistable reduction in characteristic 0}},
  journal = {Inventiones Mathematicae},
  volume = {139}, number = {2}, year = {2000}, pages = {241--273},
  doi = {10.1007/s002229900024},
  url = {https://arxiv.org/abs/alg-geom/9707012v1},
  note = {Preliminary version: arXiv:alg-geom/9707012v1}
}

@article{AtiyahSegal1968,
  author = {Atiyah, Michael F. and Segal, Graeme B.},
  title = {\href{https://doi.org/10.2307/1970716}{The index of elliptic operators. {II}}},
  journal = {Annals of Mathematics. Second Series},
  volume = {87},
  number = {3},
  year = {1968},
  pages = {531--545},
  doi = {10.2307/1970716},
  url = {https://doi.org/10.2307/1970716}
}

@article{AtiyahSinger1968,
  author = {Atiyah, Michael F. and Singer, Isadore M.},
  title = {\href{https://doi.org/10.2307/1970717}{The index of elliptic operators. {III}}},
  journal = {Annals of Mathematics. Second Series},
  volume = {87},
  number = {3},
  year = {1968},
  pages = {546--604},
  doi = {10.2307/1970717},
  url = {https://doi.org/10.2307/1970717}
}

@article{BB1973,
  author = {Bia{\l}ynicki-Birula, Andrzej},
  title = {\href{https://annals.math.princeton.edu/1973/98-3/p05}{Some theorems on actions of algebraic groups}},
  journal = {Annals of Mathematics},
  volume = {98}, number = {3}, year = {1973}, pages = {480--497},
  doi = {10.2307/1970915},
  url = {https://annals.math.princeton.edu/1973/98-3/p05}
}

@incollection{BCEKPRSW2002,
  author = {Bauer, Thomas and Campana, Fr{\'e}d{\'e}ric and Eckl, Thomas and Kebekus, Stefan and Peternell, Thomas and Rams, S{\l}awomir and Szemberg, Tomasz and Wotzlaw, Lorenz},
  title = {\href{https://arxiv.org/abs/math/0106147v1}{A reduction map for nef line bundles}},
  booktitle = {Complex Geometry: Collection of Papers Dedicated to {Hans Grauert}},
  editor = {Bauer, Ingrid and Catanese, Fabrizio and Peternell, Thomas and Kawamata, Yujiro and Siu, Yum-Tong},
  publisher = {Springer},
  address = {Berlin, Heidelberg},
  year = {2002},
  pages = {27--36},
  doi = {10.1007/978-3-642-56202-0_2},
  eprint = {math/0106147},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/math/0106147v1},
  note = {Preprint version: arXiv:math/0106147v1}
}

@article{Berndtsson2009,
  author        = {Berndtsson, Bo},
  title         = {\href{https://annals.math.princeton.edu/2009/169-2/p04}{Curvature of vector bundles associated to holomorphic fibrations}},
  journal       = {Annals of Mathematics. Second Series},
  volume        = {169},
  number        = {2},
  year          = {2009},
  pages         = {531--560},
  doi           = {10.4007/annals.2009.169.531},
  url           = {https://annals.math.princeton.edu/2009/169-2/p04}
}

@article{CDM2017,
  author = {Cao, Junyan and Demailly, Jean-Pierre and Matsumura, Shin-ichi},
  title = {\href{https://arxiv.org/abs/1703.00292v2}{A general extension theorem for cohomology classes on non reduced analytic subspaces}},
  journal = {Science China Mathematics},
  volume = {60},
  number = {6},
  year = {2017},
  pages = {949--962},
  doi = {10.1007/s11425-017-9066-0},
  eprint = {1703.00292},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1703.00292v2},
  note = {Preprint version: arXiv:1703.00292v2}
}

@incollection{CDP2015,
  author = {Campana, Fr{\'e}d{\'e}ric and Demailly, Jean-Pierre and Peternell, Thomas},
  title = {\href{https://arxiv.org/abs/1210.2092}{Rationally connected manifolds and semipositivity of the {Ricci} curvature}},
  booktitle = {Recent Advances in Algebraic Geometry: A Volume in Honor of {Rob Lazarsfeld}'s 60th Birthday},
  editor = {Hacon, Christopher D. and Musta{\c t}{\u a}, Mircea and Popa, Mihnea},
  series = {London Mathematical Society Lecture Note Series},
  volume = {417},
  publisher = {Cambridge University Press},
  address = {Cambridge},
  year = {2015},
  pages = {71--91},
  doi = {10.1017/CBO9781107416000.006},
  url = {https://arxiv.org/abs/1210.2092},
  eprint = {1210.2092},
  archivePrefix = {arXiv},
  note = {Theorem 1.4; arXiv:1210.2092v3, 5 February 2018}
}

@misc{CFSTZ2026,
  author = {Chen, Yifan and Filip, Simion and Sun, Song and Tosatti, Valentino and Zhang, Junsheng},
  title = {\href{https://arxiv.org/abs/2609.26716}{Compact {K\"ahler} surfaces with semipositive anticanonical bundle}},
  year = {2026},
  eprint = {2609.26716},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  note = {Version 1, 22 September 2026},
  url = {https://arxiv.org/abs/2609.26716}
}

@article{DPS1996,
  author = {Demailly, Jean-Pierre and Peternell, Thomas and Schneider, Michael},
  title = {\href{https://www.numdam.org/item/CM_1996__101_2_217_0/}{Compact {K\"ahler} manifolds with hermitian semipositive anticanonical bundle}},
  journal = {Compositio Mathematica},
  volume = {101},
  number = {2},
  year = {1996},
  pages = {217--224},
  url = {https://www.numdam.org/item/CM_1996__101_2_217_0/}
}

@article{DPS2001,
  author = {Demailly, Jean-Pierre and Peternell, Thomas and Schneider, Michael},
  title = {\href{https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/dps5.pdf}{Pseudo-effective line bundles on compact {K\"ahler} manifolds}},
  journal = {International Journal of Mathematics},
  volume = {12},
  number = {6},
  year = {2001},
  pages = {689--741},
  doi = {10.1142/S0129167X01000861},
  url = {https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/dps5.pdf},
  eprint = {math/0006205},
  archivePrefix = {arXiv}
}

@misc{Demailly2011,
  author = {Demailly, Jean-Pierre},
  title = {\href{https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/analmeth_book.pdf}{Analytic Methods in Algebraic Geometry}},
  year = {2011},
  month = jul,
  howpublished = {Author manuscript},
  note = {Manuscript dated July 2011; Lemma 5.6(a), pp. 35--36, and Theorem 5.11, p. 39},
  url = {https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/analmeth_book.pdf}
}

@misc{Demailly2012,
  author        = {Demailly, Jean-Pierre},
  title         = {\href{https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf}{Complex Analytic and Differential Geometry}},
  year          = {2012},
  howpublished  = {Author's online book},
  url           = {https://www-fourier.univ-grenoble-alpes.fr/~demailly/manuscripts/agbook.pdf},
  note          = {Version of 21 June 2012}
}

@incollection{Dolgachev2016,
  author = {Dolgachev, Igor V.},
  title = {\href{https://arxiv.org/abs/1412.7744}{A brief introduction to {Enriques} surfaces}},
  booktitle = {Development of Moduli Theory---Kyoto 2013},
  series = {Advanced Studies in Pure Mathematics},
  volume = {69},
  publisher = {Mathematical Society of Japan},
  address = {Tokyo},
  year = {2016},
  pages = {1--32},
  url = {https://arxiv.org/abs/1412.7744},
  eprint = {1412.7744},
  archivePrefix = {arXiv}
}

@article{EKL1995,
  author = {Ein, Lawrence and K{\"u}chle, Oliver and Lazarsfeld, Robert},
  title = {\href{https://arxiv.org/abs/alg-geom/9408003v1}{Local positivity of ample line bundles}},
  journal = {Journal of Differential Geometry},
  volume = {42},
  number = {2},
  year = {1995},
  pages = {193--219},
  doi = {10.4310/jdg/1214457231},
  eprint = {alg-geom/9408003},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/alg-geom/9408003v1},
  note = {Preprint version: arXiv:alg-geom/9408003v1}
}

@article{FM2016,
  author = {Fujino, Osamu and Matsumura, Shin-ichi},
  title = {\href{https://arxiv.org/abs/1605.02284v3}{Injectivity theorem for pseudo-effective line bundles and its applications}},
  journal = {Transactions of the American Mathematical Society, Series B},
  volume = {8},
  year = {2021},
  pages = {849--884},
  doi = {10.1090/btran/86},
  eprint = {1605.02284v3},
  archivePrefix = {arXiv},
  primaryClass = {math.CV},
  url = {https://arxiv.org/abs/1605.02284v3},
  note = {Author version: arXiv:1605.02284v3, 21 May 2022}
}

@article{Fujino2018,
  author = {Fujino, Osamu},
  title = {\href{https://www.math.kyoto-u.ac.jp/~fujino/kollar-nadel.pdf}{{Koll\'ar--Nadel} Type Vanishing Theorem}},
  journal = {Southeast Asian Bulletin of Mathematics},
  volume = {42},
  number = {5},
  year = {2018},
  pages = {643--646},
  url = {https://www.math.kyoto-u.ac.jp/~fujino/kollar-nadel.pdf}
}

@article{Fujisawa2015,
  author = {Fujisawa, Taro},
  title = {\href{https://arxiv.org/abs/1512.03887v1}{A remark on the decomposition theorem for direct images of canonical sheaves tensorized with semipositive vector bundles}},
  journal = {Proceedings of the Japan Academy, Series A, Mathematical Sciences},
  volume = {92}, number = {7}, pages = {84--85}, year = {2016},
  doi = {10.3792/pjaa.92.84},
  eprint = {1512.03887v1}, archivePrefix = {arXiv},
  note = {Theorem 1 is cited from arXiv version 1},
  url = {https://arxiv.org/abs/1512.03887v1}
}

@article{GuanZhou2015,
  author = {Guan, Qi'an and Zhou, Xiangyu},
  title = {\href{https://annals.math.princeton.edu/wp-content/uploads/annals-v182-n2-p05-p.pdf}{A proof of {Demailly}'s strong openness conjecture}},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {182},
  number = {2},
  year = {2015},
  pages = {605--616},
  doi = {10.4007/annals.2015.182.2.5},
  url = {https://annals.math.princeton.edu/wp-content/uploads/annals-v182-n2-p05-p.pdf}
}

@misc{Kleiman2005,
  author = {Kleiman, Steven L.},
  title = {\href{https://arxiv.org/abs/math/0504020v1}{The {Picard} scheme}},
  year = {2005},
  eprint = {math/0504020},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/math/0504020v1},
  note = {Version: arXiv:math/0504020v1, 1 April 2005}
}

@article{LMPTX2023,
  author = {Lazi{\'c}, Vladimir and Matsumura, Shin-ichi and Peternell, Thomas and Tsakanikas, Nikolaos and Xie, Zhixin},
  title = {\href{https://ems.press/content/serial-article-files/31138}{The Nonvanishing Problem for varieties with nef anticanonical bundle}},
  journal = {Documenta Mathematica},
  volume = {28},
  number = {6},
  year = {2023},
  pages = {1393--1440},
  doi = {10.4171/DM/936},
  url = {https://ems.press/content/serial-article-files/31138},
  eprint = {2202.13814},
  archivePrefix = {arXiv}
}

@article{Lehmann2015,
  author = {Lehmann, Brian},
  title = {\href{https://arxiv.org/abs/1109.4382v3}{Numerical triviality and pullbacks}},
  journal = {Journal of Pure and Applied Algebra},
  volume = {219},
  number = {12},
  year = {2015},
  pages = {5637--5649},
  doi = {10.1016/j.jpaa.2015.05.037},
  eprint = {1109.4382},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1109.4382v3},
  note = {Preprint version: arXiv:1109.4382v3}
}

@article{Matsumura2018,
  author        = {Matsumura, Shin-ichi},
  title         = {\href{https://arxiv.org/abs/1511.04222v3}{A vanishing theorem of {Koll\'ar--Ohsawa} type}},
  journal       = {Mathematische Annalen},
  volume        = {366},
  number        = {3-4},
  year          = {2016},
  pages         = {1451--1465},
  eprint        = {1511.04222v3},
  archivePrefix = {arXiv},
  primaryClass  = {math.CV},
  doi           = {10.1007/s00208-016-1371-8},
  url           = {https://arxiv.org/abs/1511.04222v3},
  note          = {Preprint version: arXiv:1511.04222v3, 26 January 2018; Theorem 1.3}
}

@misc{MengQingZhou2026,
  author = {Meng, Xiankui and Qing, Chenghao and Zhou, Xiangyu},
  title = {\href{https://arxiv.org/abs/2602.13821}{Vanishing theorems for pseudo-effective line bundles}},
  year = {2026},
  eprint = {2602.13821},
  archivePrefix = {arXiv},
  primaryClass = {math.CV},
  note = {Version 2, 10 July 2026},
  url = {https://arxiv.org/abs/2602.13821}
}

@article{Muller2025,
  author = {M{\"u}ller, Niklas},
  title = {\href{https://arxiv.org/abs/2305.19109}{Two non-vanishing results concerning the anti-canonical bundle}},
  journal = {Nagoya Mathematical Journal},
  volume = {258},
  year = {2025},
  pages = {201--218},
  doi = {10.1017/nmj.2024.21},
  url = {https://arxiv.org/abs/2305.19109},
  eprint = {2305.19109},
  archivePrefix = {arXiv}
}

@article{Nadel1990,
  author = {Nadel, Alan Michael},
  title = {\href{https://annals.math.princeton.edu/1990/132-3/p04}{Multiplier ideal sheaves and {K\"ahler--Einstein} metrics of positive scalar curvature}},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {132},
  number = {3},
  year = {1990},
  pages = {549--596},
  doi = {10.2307/1971429},
  url = {https://annals.math.princeton.edu/1990/132-3/p04}
}

@article{PT2018,
  author = {P{\u a}un, Mihai and Takayama, Shigeharu},
  title = {\href{https://arxiv.org/abs/1409.5504v1}{Positivity of twisted relative pluricanonical bundles and their direct images}},
  journal = {Journal of Algebraic Geometry},
  volume = {27}, number = {2}, year = {2018}, pages = {211--272},
  doi = {10.1090/jag/702},
  url = {https://arxiv.org/abs/1409.5504v1},
  note = {Preprint version: arXiv:1409.5504v1, 19 September 2014}
}

@article{Richberg1968,
  author        = {Richberg, Rolf},
  title         = {\href{https://link.springer.com/article/10.1007/BF02063212}{Stetige streng pseudokonvexe {Funktionen}}},
  journal       = {Mathematische Annalen},
  volume        = {175},
  year          = {1967},
  pages         = {257--286},
  doi           = {10.1007/BF02063212},
  url           = {https://link.springer.com/article/10.1007/BF02063212},
  note          = {Also commonly cited with the year 1968}
}

@misc{StacksNormNormal,
  author = {{The Stacks Project Authors}},
  title = {\href{https://stacks.math.columbia.edu/tag/0BD3}{The {Stacks Project}, Lemma 31.18.7}},
  year = {2026},
  url = {https://stacks.math.columbia.edu/tag/0BD3},
  note = {Tag 0BD3}
}

@article{Yau1978,
  author = {Yau, Shing-Tung},
  title = {\href{https://doi.org/10.1002/cpa.3160310304}{On the {Ricci} curvature of a compact {K\"ahler} manifold and the complex {Monge--Amp\`ere} equation. {I}}},
  journal = {Communications on Pure and Applied Mathematics},
  volume = {31},
  number = {3},
  year = {1978},
  pages = {339--411},
  doi = {10.1002/cpa.3160310304},
  url = {https://doi.org/10.1002/cpa.3160310304}
}

@incollection{Yau1994,
  author = {Yau, Shing-Tung},
  title = {\href{https://www.intlpress.com/site/pub/files/preview/bookpubs/00000308.pdf}{Open problems in geometry}},
  booktitle = {Lectures on Differential Geometry},
  series = {Conference Proceedings and Lecture Notes in Geometry and Topology},
  volume = {1},
  publisher = {International Press},
  address = {Cambridge, MA},
  year = {1994},
  pages = {365--404},
  isbn = {9781571460127},
  note = {In the book by Richard Schoen and Shing-Tung Yau; Problem 75, p.~395},
  url = {https://www.intlpress.com/site/pub/files/preview/bookpubs/00000308.pdf}
}

@incollection{Grothendieck1961Hilbert,
  author = {Grothendieck, Alexander},
  title = {\href{https://www.numdam.org/item/SB_1960-1961__6__249_0/}{Techniques de construction et th{\'e}or{\`e}mes d'existence en g{\'e}om{\'e}trie alg{\'e}brique {IV}: les sch{\'e}mas de {Hilbert}}},
  booktitle = {S{\'e}minaire Bourbaki: ann{\'e}es 1960/61, expos{\'e}s 205--222},
  series = {S{\'e}minaire Bourbaki},
  number = {6},
  year = {1961},
  pages = {249--276},
  publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France},
  address = {Paris},
  note = {Expos{\'e} 221},
  url = {https://www.numdam.org/item/SB_1960-1961__6__249_0/}
}

@article{Kodaira1954,
 author = {Kodaira, Kunihiko},
 doi = {10.1073/pnas.40.5.313},
 journal = {Proceedings of the National Academy of Sciences of the United States of America},
 number = {5},
 pages = {313--316},
 title = {\href{https://doi.org/10.1073/pnas.40.5.313}{On {K\"ahler} varieties of restricted type}},
 url = {https://doi.org/10.1073/pnas.40.5.313},
 volume = {40},
 year = {1954}
}

@article{Zassenhaus1948,
 author = {Zassenhaus, Hans},
 journal = {Commentarii Mathematici Helvetici},
 pages = {117--141},
 title = {\href{https://www.e-periodica.ch/cntmng?pid=com-001\%3A1948\%3A21\%3A\%3A13}{{\"U}ber einen Algorithmus zur Bestimmung der Raumgruppen}},
 url = {https://www.e-periodica.ch/cntmng?pid=com-001\%3A1948\%3A21\%3A\%3A13},
 volume = {21},
 year = {1948}
}

@article{BaldoniBerlineDeLoeraKoeppeVergne2012,
  author = {Baldoni, Velleda and Berline, Nicole and De Loera, Jes{\'u}s A. and K{\"o}ppe, Matthias and Vergne, Mich{\`e}le},
  title = {\href{https://arxiv.org/abs/1011.1602v1}{Computation of the highest coefficients of weighted {Ehrhart} quasi-polynomials of rational polyhedra}},
  journal = {Foundations of Computational Mathematics},
  volume = {12},
  number = {4},
  year = {2012},
  pages = {435--469},
  doi = {10.1007/s10208-011-9106-4},
  eprint = {1011.1602},
  archivePrefix = {arXiv},
  primaryClass = {math.CO},
  url = {https://arxiv.org/abs/1011.1602v1},
  note = {Preprint version: arXiv:1011.1602v1, 7 November 2010}
}

@article{LP2018,
  author = {Lazi{\'c}, Vladimir and Peternell, Thomas},
  title = {\href{https://epiga.episciences.org/4276/pdf}{Abundance for varieties with many differential forms}},
  journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
  volume = {2},
  year = {2018},
  pages = {Article 1, 35 pp.},
  doi = {10.46298/epiga.2018.volume2.3867},
  url = {https://epiga.episciences.org/4276/pdf}
}

@article{BP2008,
  author = {Berndtsson, Bo and P{\u a}un, Mihai},
  title = {\href{https://arxiv.org/abs/math/0703344v4}{Bergman kernels and the pseudoeffectivity of relative canonical bundles}},
  journal = {Duke Mathematical Journal},
  volume = {145}, number = {2}, year = {2008}, pages = {341--378},
  url = {https://arxiv.org/abs/math/0703344v4},
  note = {Preprint version: arXiv:math/0703344v4, 21 January 2008}
}

@article{Mourougane1999,
  author = {Mourougane, Christophe},
  title = {\href{https://doi.org/10.24033/bsmf.2344}{Th\'eor\`emes d'annulation g\'en\'erique pour les fibr\'es vectoriels semi-n\'egatifs}},
  journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
  volume = {127}, number = {1}, year = {1999}, pages = {115--133},
  doi = {10.24033/bsmf.2344},
  url = {https://numdam.org/articles/10.24033/bsmf.2344/}
}

@article{Ou2023,
  author = {Ou, Wenhao},
  title = {\href{https://arxiv.org/abs/1703.03175v4}{On generic nefness of tangent sheaves}},
  journal = {Mathematische Zeitschrift},
  volume = {304}, number = {4}, year = {2023},
  pages = {Paper No.~58},
  doi = {10.1007/s00209-023-03306-6},
  url = {https://arxiv.org/abs/1703.03175v4},
  note = {Preprint version: arXiv:1703.03175v4, 2 August 2021}
}

@misc{CompanionH,
  author = {{OpenAI}},
  title = {{Anticanonical nonvanishing from smooth semipositivity}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026/main.pdf}{OAI:Anticanonical-nonvanishing-from-smooth-semipositivity-September-26-2026}},
  year = {2026}
}
@misc{CompanionI,
  author = {{OpenAI}},
  title = {{Invariant anticanonical indices and conversion of twisted differentials}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026/main.pdf}{OAI:Invariant-anticanonical-indices-and-conversion-of-twisted-differentials-September-26-2026}},
  year = {2026}
}