@article{Bridgeland2007,
  author = {Bridgeland, Tom},
  title = {Stability conditions on triangulated categories},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {166},
  number = {2},
  year = {2007},
  pages = {317--345},
  doi = {10.4007/annals.2007.166.317},
  note = {\url{https://doi.org/10.4007/annals.2007.166.317}},
  url = {https://annals.math.princeton.edu/2007/166-2/p01}
}

@article{HappelReitenSmalo1996,
  author = {Happel, Dieter and Reiten, Idun and Smal{\o}, Sverre O.},
  title = {Tilting in abelian categories and quasitilted algebras},
  journal = {Memoirs of the American Mathematical Society},
  volume = {120},
  number = {575},
  pages = {viii+88},
  year = {1996},
  doi = {10.1090/memo/0575},
  note = {\url{https://doi.org/10.1090/memo/0575}},
  url = {https://doi.org/10.1090/memo/0575}
}

@article{SeidelThomas2001,
  author = {Seidel, Paul and Thomas, Richard P.},
  title = {Braid group actions on derived categories of coherent sheaves},
  journal = {Duke Mathematical Journal},
  volume = {108},
  number = {1},
  year = {2001},
  pages = {37--108},
  doi = {10.1215/S0012-7094-01-10812-0},
  note = {\url{https://doi.org/10.1215/S0012-7094-01-10812-0}},
  eprint = {math/0001043},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/math/0001043}
}

@incollection{Orlov2009,
  author = {Orlov, Dmitri},
  title = {Derived categories of coherent sheaves and triangulated categories of singularities},
  booktitle = {Algebra, Arithmetic, and Geometry: In Honor of {Yu. I. Manin}},
  editor = {Tschinkel, Yuri and Zarhin, Yuri},
  series = {Progress in Mathematics},
  volume = {270},
  publisher = {Birkh{\"a}user},
  address = {Boston, MA},
  year = {2009},
  pages = {503--531},
  doi = {10.1007/978-0-8176-4747-6_16},
  note = {\url{https://doi.org/10.1007/978-0-8176-4747-6_16}},
  eprint = {math/0503632},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/math/0503632}
}

@article{BayerMacriToda2014,
  author = {Bayer, Arend and Macr{\`i}, Emanuele and Toda, Yukinobu},
  title = {{Bridgeland} stability conditions on threefolds {I}: {Bogomolov--Gieseker} type inequalities},
  journal = {Journal of Algebraic Geometry},
  volume = {23},
  number = {1},
  year = {2014},
  pages = {117--163},
  doi = {10.1090/S1056-3911-2013-00617-7},
  note = {\url{https://doi.org/10.1090/S1056-3911-2013-00617-7}},
  eprint = {1103.5010},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1103.5010v2}
}

@misc{Toda2013,
  author = {Toda, Yukinobu},
  title = {{Gepner} type stability conditions on graded matrix factorizations},
  year = {2013},
  eprint = {1302.6293v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  doi = {10.48550/arXiv.1302.6293},
  url = {https://arxiv.org/abs/1302.6293v1},
  note = {\href{https://arxiv.org/abs/1302.6293v1}{arXiv:1302.6293v1}. Version 1, 26 February 2013}
}

@misc{TodaQuintic2013,
  author = {Toda, Yukinobu},
  title = {{Gepner} point and strong {Bogomolov--Gieseker} inequality for quintic 3-folds},
  year = {2013},
  eprint = {1305.0345v3},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  doi = {10.48550/arXiv.1305.0345},
  url = {https://arxiv.org/abs/1305.0345v3},
  note = {\href{https://arxiv.org/abs/1305.0345v3}{arXiv:1305.0345v3}. Version 3, 7 May 2013; first posted 2 May 2013}
}

@article{Li2019,
  author = {Li, Chunyi},
  title = {On stability conditions for the quintic threefold},
  journal = {Inventiones Mathematicae},
  volume = {218},
  number = {1},
  year = {2019},
  pages = {301--340},
  doi = {10.1007/s00222-019-00888-z},
  note = {\url{https://doi.org/10.1007/s00222-019-00888-z}},
  eprint = {1810.03434},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1810.03434v2}
}

@misc{Xu2026,
  author = {Xu, Chunkai},
  title = {Stronger {Bogomolov--Gieseker} type inequality on quintic threefold},
  year = {2026},
  eprint = {2511.21288v2},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  doi = {10.48550/arXiv.2511.21288},
  url = {https://arxiv.org/abs/2511.21288v2},
  note = {\href{https://arxiv.org/abs/2511.21288v2}{arXiv:2511.21288v2}. Version 2, 4 January 2026; first posted 26 November 2025}
}

@article{Tattar2021,
  author = {Tattar, Aran},
  title = {Torsion pairs and quasi-abelian categories},
  journal = {Algebras and Representation Theory},
  volume = {24},
  year = {2021},
  pages = {1557--1581},
  doi = {10.1007/s10468-020-10004-y},
  note = {\url{https://doi.org/10.1007/s10468-020-10004-y}},
  url = {https://link.springer.com/article/10.1007/s10468-020-10004-y}
}

@article{Douglas2001,
  author = {Douglas, Michael R.},
  title = {D-branes, Categories and {N=1} Supersymmetry},
  journal = {Journal of Mathematical Physics},
  volume = {42},
  year = {2001},
  pages = {2818--2843},
  doi = {10.1063/1.1374448},
  note = {\url{https://doi.org/10.1063/1.1374448}},
  eprint = {hep-th/0011017},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/0011017v4}
}

@misc{KontsevichSoibelman2008,
  author = {Kontsevich, Maxim and Soibelman, Yan},
  title = {Stability structures, motivic {Donaldson--Thomas} invariants and cluster transformations},
  year = {2008},
  note = {\href{https://arxiv.org/abs/0811.2435v1}{arXiv:0811.2435v1}},
  eprint = {0811.2435},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/0811.2435v1}
}

@article{BallardFaveroKatzarkov2012,
  author = {Ballard, Matthew and Favero, David and Katzarkov, Ludmil},
  title = {{Orlov} spectra: bounds and gaps},
  journal = {Inventiones Mathematicae},
  volume = {189},
  year = {2012},
  pages = {359--430},
  eprint = {1012.0864v3},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1012.0864v3},
  note = {\href{https://arxiv.org/abs/1012.0864v3}{arXiv:1012.0864v3}. Version 3, 14 October 2013}
}

@misc{Aspinwall2004,
  author = {Aspinwall, Paul S.},
  title = {{D}-branes on {Calabi--Yau} manifolds},
  year = {2004},
  eprint = {hep-th/0403166v1},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/hep-th/0403166v1},
  note = {\href{https://arxiv.org/abs/hep-th/0403166v1}{arXiv:hep-th/0403166v1}. Version 1, 16 March 2004}
}

@article{BorelSerre1958,
  author = {Borel, Armand and Serre, Jean-Pierre},
  title = {Le th{\'e}or{\`e}me de {Riemann--Roch}},
  journal = {Bulletin de la Soci{\'e}t{\'e} Math{\'e}matique de France},
  volume = {86},
  year = {1958},
  pages = {97--136},
  note = {\url{https://www.numdam.org/item/BSMF_1958__86__97_0/}},
  url = {https://www.numdam.org/item/BSMF_1958__86__97_0/}
}

@misc{Catanese2014,
  author = {Catanese, Fabrizio},
  title = {Topological methods in moduli theory},
  year = {2014},
  eprint = {1411.3235v1},
  archivePrefix = {arXiv},
  primaryClass = {math.AG},
  url = {https://arxiv.org/abs/1411.3235v1},
  note = {\href{https://arxiv.org/abs/1411.3235v1}{arXiv:1411.3235v1}. Version 1}
}