@article{AtiyahSegal1968,
  author = {Atiyah, Michael F. and Segal, Graeme B.},
  title = {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 = {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{Berndtsson2009,
  author = {Berndtsson, Bo},
  title = {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},
  eprint = {math/0511225},
  archivePrefix = {arXiv}
}

@incollection{CDP2015,
  author = {Campana, Fr{\'e}d{\'e}ric and Demailly, Jean-Pierre and Peternell, Thomas},
  title = {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}
}

@article{DPS1996,
  author = {Demailly, Jean-Pierre and Peternell, Thomas and Schneider, Michael},
  title = {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 = {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}
}

@incollection{Dolgachev2016,
  author = {Dolgachev, Igor V.},
  title = {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{Fujino2018,
  author = {Fujino, Osamu},
  title = {{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},
  eprint = {1607.04684},
  archivePrefix = {arXiv}
}

@article{LMPTX2023,
  author = {Lazi{\'c}, Vladimir and Matsumura, Shin-ichi and Peternell, Thomas and Tsakanikas, Nikolaos and Xie, Zhixin},
  title = {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}
}

@incollection{Grothendieck1961Hilbert,
  author = {Grothendieck, Alexander},
  title = {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{Muller2025,
  author = {M{\"u}ller, Niklas},
  title = {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{Ou2023,
  author = {Ou, Wenhao},
  title = {On generic nefness of tangent sheaves},
  journal = {Mathematische Zeitschrift},
  volume = {304},
  year = {2023},
  pages = {Paper No. 58},
  doi = {10.1007/s00209-023-03306-6},
  url = {https://arxiv.org/abs/1703.03175},
  eprint = {1703.03175},
  archivePrefix = {arXiv}
}

@article{Skoda1972,
  author = {Skoda, Henri},
  title = {Sous-ensembles analytiques d'ordre fini ou infini dans {$\mathbb{C}^n$}},
  journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume = {100},
  year = {1972},
  pages = {353--408},
  doi = {10.24033/bsmf.1743},
  url = {https://www.numdam.org/articles/10.24033/bsmf.1743/}
}

@article{Yau1978,
  author = {Yau, Shing-Tung},
  title = {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 = {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}
}

@article{LP2018,
  author = {Lazi{\'c}, Vladimir and Peternell, Thomas},
  title = {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}
}

@misc{CFSTZ2026,
  author = {Chen, Yifan and Filip, Simion and Sun, Song and Tosatti, Valentino and Zhang, Junsheng},
  title = {Compact {K\"ahler} surfaces with semipositive anticanonical bundle},
  year = {2026},
  eprint = {2609.26716},
  archivePrefix = {arXiv},
  primaryClass = {math.DG},
  note = {\href{https://arxiv.org/abs/2609.26716}{arXiv:2609.26716v1}, 22 September 2026},
  url = {https://arxiv.org/abs/2609.26716}
}

@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 = {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},
  note = {Preprint version arXiv:1011.1602v1, 7 November 2010},
  url = {https://doi.org/10.1007/s10208-011-9106-4}
}

@article{AtiyahBott1966,
  author = {Atiyah, Michael F. and Bott, Raoul},
  title = {A {Lefschetz} fixed point formula for elliptic differential operators},
  journal = {Bulletin of the American Mathematical Society},
  volume = {72},
  number = {2},
  year = {1966},
  pages = {245--250},
  doi = {10.1090/S0002-9904-1966-11483-0}
}

@article{Stanley1974Reciprocity,
  author = {Stanley, Richard P.},
  title = {Combinatorial reciprocity theorems},
  journal = {Advances in Mathematics},
  volume = {14},
  number = {2},
  year = {1974},
  pages = {194--253},
  doi = {10.1016/0001-8708(74)90030-9},
  url = {https://math.mit.edu/~rstan/pubs/pubfiles/22.pdf}
}

@article{Mourougane1999,
  author = {Mourougane, Christophe},
  title = {Th{\'e}or{\`e}mes d'annulation g{\'e}n{\'e}rique pour les fibr{\'e}s vectoriels semi-n{\'e}gatifs},
  journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume = {127},
  number = {1},
  year = {1999},
  pages = {115--133},
  doi = {10.24033/bsmf.2344},
  url = {https://www.numdam.org/article/BSMF_1999__127_1_115_0.pdf}
}


@article{Takegoshi1997,
  author = {Takegoshi, Kensho},
  title = {On cohomology groups of nef line bundles tensorized with multiplier ideal sheaves on compact {K\"ahler} manifolds},
  journal = {Osaka Journal of Mathematics},
  volume = {34},
  number = {4},
  year = {1997},
  pages = {783--802},
  url = {https://ocu-omu.repo.nii.ac.jp/record/2009615/files/111F0000002-03404-4.pdf}
}


@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}
}

@article{DemaillyKollar2001,
 author={Demailly, Jean-Pierre and Koll{\'a}r, J{\'a}nos},
 title={Semi-continuity of complex singularity exponents and {K\"ahler--Einstein} metrics on {Fano} orbifolds},
 journal={Annales scientifiques de l'{\'E}cole Normale Sup{\'e}rieure. S{\'e}rie 4},
 volume={34},
 number={4},
 year={2001},
 pages={525--556},
 doi={10.1016/S0012-9593(01)01069-2},
 url={https://www.numdam.org/item/ASENS_2001_4_34_4_525_0/},
 eprint={math/9910118},
 archivePrefix={arXiv},
 note={Elementary properties 1.4(8); arXiv:math/9910118v3, 14 November 2013}
}