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Symplectic rigidity of O'Grady's tenfolds

Luca Giovenzana, Annalisa Grossi, Claudio Onorati, Davide Cesare Veniani

Abstract

We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.

Symplectic rigidity of O'Grady's tenfolds

Abstract

We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.
Paper Structure (9 sections, 4 theorems, 19 equations, 1 table)

This paper contains 9 sections, 4 theorems, 19 equations, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Lattices
  4. Torelli theorem
  5. Leech lattice
  6. Sphere packings
  7. Proof of \ref{['thm:main.aut.symp.OG10']}
  8. Trivial action on discriminant group
  9. Non-trivial action on discriminant group

Key Result

theorem 1

If $X$ is a complex manifold of type $\OG10$, and $f \in \Aut(X)$ is a symplectic automorphism of finite order, then $f$ is the identity.

Theorems & Definitions (7)

  • theorem 1
  • theorem 2
  • proof
  • theorem 3
  • remark 1
  • proposition 1: Gaberdiel.Hohenegger.Volpato:symmetries.K3.sigma.models,Huybrechts:derived.cat.K3.sp.aut.Conway.group
  • proof