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arXiv · 2310.06580

Finite groups of symplectic birational transformations of IHS manifolds of $OG10$ type

Lisa Marquand·Stevell Muller
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Abstract

We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of OG10 type. In particular, if X is an IHS manifold of OG10 type and G a finite subgroup of symplectic birational transformations of X, then the action of G on H2(X, Z) is conjugate to a subgroup of one of 375 groups of isometries. We prove a criterion for when such a group is determined by a group of automorphisms acting on a cubic fourfold, and apply it to our classification. Our proof is computer aided and our results are available in a Zenodo dataset.

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Lisa Marquand, Stevell Muller. 2023-10-10. Finite groups of symplectic birational transformations of IHS manifolds of $OG10$ type. https://arxiv.org/abs/2310.06580

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