On Symplectic Birational Self-Maps of Projective Hyperkähler Manifolds of K3[n]-Type

Abstract We prove that projective hyperkähler 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 c...

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Bibliographic Details
Published in:International mathematics research notices 2024-08, Vol.2024 (15), p.11064-11081
Main Authors: Dutta, Yajnaseni, Mattei, Dominique, Prieto-Montañez, Yulieth
Format: Article
Language:English
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Summary:Abstract We prove that projective hyperkähler 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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnae112