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On entropy of spherical twists

Author: Genki Ouchi; with an appendix by Arend Bayer
Journal: Proc. Amer. Math. Soc. 148 (2020), 1003-1014
MSC (2010): Primary 14F05
Published electronically: October 18, 2019
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Abstract: In this paper, we compute categorical entropy of spherical twists. In particular, we prove that the Gromov-Yomdin-type conjecture holds for spherical twists. Moreover, we construct counterexamples of Gromov-Yomdin type conjecture for K3 surfaces modifying Fan's construction for even higher-dimensional Calabi-Yau manifolds.

The appendix, by Arend Bayer, shows the nonemptiness of complements of a number of spherical objects in the derived categories of K3 surfaces.

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Additional Information

Genki Ouchi
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo 153-8914, Japan
Address at time of publication: RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, 2F Main Research Building, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan

Arend Bayer
Affiliation: School of Mathematics and Maxwell Institute, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom

Received by editor(s): September 27, 2017
Received by editor(s) in revised form: July 9, 2019
Published electronically: October 18, 2019
Additional Notes: This work was supported by Grant-in-Aid for JSPS Research Fellow 15J08505.
Communicated by: Lev Borisov
Article copyright: © Copyright 2019 American Mathematical Society