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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
- 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!
- Subjects :
- Mathematics - Algebraic Geometry
14J50, 14E05, 14D20, 14C05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2209.03783
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1093/imrn/rnae112