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On symplectic birational self-maps of projective hyperk\'{a}hler manifolds of K3$^{[n]}$-type

On symplectic birational self-maps of projective hyperk\'{a}hler manifolds of K3$^{[n]}$-type

Authors :
Dutta, Yajnaseni
Mattei, Dominique
Prieto-MontaƱez, Yulieth
Publication Year :
2022

Abstract

We prove that projective hyperk\"{a}hler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we analyze the reflections on the movable cone of moduli spaces of sheaves and determine when they come from a birational involution.<br />Comment: 21 pages, v2: Theorem A significantly improved, Theorem B updated to reflect one of its consequences. v3: The numerical criterion in Lemma 4.13 (and formerly Theorem C) has been significantly simplified. Feedback from anonymous referees incorporated. Comments are still very welcome!

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2209.03783
Document Type :
Working Paper
Full Text :
https://doi.org/10.1093/imrn/rnae112