Non-commutative deformations of perverse coherent sheaves and rational curves

Kawamata, Yujiro

doi:10.1090/jag/805

Author: Yujiro Kawamata
Journal: J. Algebraic Geom. 32 (2023), 59-91
DOI: https://doi.org/10.1090/jag/805
Published electronically: May 17, 2022
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Abstract | References | Additional Information

Abstract: We consider non-commutative deformations of sheaves on algebraic varieties. We develop some tools to determine parameter algebras of versal non-commutative deformations for partial simple collections and the structure sheaves of smooth rational curves. We apply them to universal flopping contractions of length $2$ and higher. We confirm Donovan-Wemyss conjecture in the case of deformations of Laufer’s flops.

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Additional Information

Yujiro Kawamata
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo 153-8914 Japan; Morningside Center of Mathematics, Chinese Academy of Sciences, Haidian District, Beijing 100190, People’s Republic of China; Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea; and National Center for Theoretical Sciences, Mathematics Division, National Taiwan University, Taipei 106, Taiwan
MR Author ID: 99410
Email: kawamata@ms.u-tokyo.ac.jp

Received by editor(s): June 17, 2020
Published electronically: May 17, 2022
Additional Notes: This work was partly supported by JSPS Grant-in-Aid 16H02141.
Article copyright: © Copyright 2022 University Press, Inc.