O'Grady tenfolds as moduli spaces of sheaves

被引：1
作者：
Felisetti, Camilla [1 ]
Giovenzana, Franco [2 ]
Grossi, Annalisa [2 ]
机构：
[1] Univ Modena & Reggio Emilia, Dipartimento Sci Fis Informat & Matemat, Via Campi 213-B, I-41125 Modena, Italy
[2] Univ Paris Saclay, Lab Math Orsay, Rue Michel Magat, Bat 307, F-91405 Orsay, France
来源：
FORUM OF MATHEMATICS SIGMA | 2024年 / 12卷
基金：
欧洲研究理事会;
关键词：
14J42; 14E07; 14J50; BIRATIONAL GEOMETRY; MONODROMY; STABILITY; TORELLI; ORDER;
D O I：
10.1017/fms.2024.46
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give a lattice-theoretic characterization for a manifold of $\operatorname {\mathrm {OG10}}$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\operatorname {\mathrm {OG10}}$ type associated to any smooth cubic fourfold. Moreover, we determine when a birational transformation is induced by an automorphism of the K3 surface, and we use this to classify all induced birational symplectic involutions.
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页数：20
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