Homological Bondal-Orlov localization conjecture for rational singularities
Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66.
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Author
Mauri, MirkoISTA;
Shinder, Evgeny
Department
Abstract
Given a resolution of rational singularities π:X~→X over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor Rπ∗:Db(X~)→Db(X)
between bounded derived categories of coherent sheaves generates Db(X)
as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms π:X~→X , with X~
smooth, satisfying Rπ∗(OX~)=OX .
Publishing Year
Date Published
2023-08-03
Journal Title
Forum of Mathematics, Sigma
Acknowledgement
We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara, Sándor Kovács, Alexander Kuznetsov, Mircea Musta ă, Nebojsa Pavic, Pavel Sechin, and Michael Wemyss for discussions and e-mail correspondence. We also thank the anonymous referee for the helpful comments. M.M. was supported by the Institute of Science and Technology Austria. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 101034413. E.S. was partially supported by the EPSRC grant EP/T019379/1 “Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties.”
Volume
11
Article Number
e66
eISSN
IST-REx-ID
Cite this
Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.65
Mauri, M., & Shinder, E. (2023). Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.65
Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” Forum of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.65.
M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture for rational singularities,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023.
Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture for rational singularities. Forum of Mathematics, Sigma. 11, e66.
Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture for Rational Singularities.” Forum of Mathematics, Sigma, vol. 11, e66, Cambridge University Press, 2023, doi:10.1017/fms.2023.65.
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