A trichotomy for the autoequivalence groups on smooth projective surfaces
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Abstract:
We study autoequivalence groups of the derived categories on smooth projective surfaces. We show a trichotomy of types according to the maximal dimension of Fourier–Mukai kernels for autoequivalences. This number is $2$, $3$, or $4$, and we also pose a conjecture on the description of autoequivalence groups if it is $2$, and prove it in some special cases.References
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Additional Information
- Hokuto Uehara
- Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minamiohsawa, Hachioji-shi, Tokyo, 192-0397, Japan
- MR Author ID: 663390
- Email: hokuto@tmu.ac.jp
- Received by editor(s): April 7, 2017
- Received by editor(s) in revised form: August 25, 2017, and October 2, 2017
- Published electronically: October 1, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 3529-3547
- MSC (2010): Primary 14F05, 18E30
- DOI: https://doi.org/10.1090/tran/7439
- MathSciNet review: 3896121