January, 2025 Irreducible holomorphic symplectic manifolds with an action of Z34:A6
Paola COMPARIN, Romain DEMELLE, Pablo QUEZADA MORA
Author Affiliations +
J. Math. Soc. Japan Advance Publication 1-19 (January, 2025). DOI: 10.2969/jmsj/93409340

Abstract

Höhn and Mason classified the groups acting symplectically on an irreducible holomorphic symplectic (IHS) manifold of K3[2]-type, finding that Z34:A6 is the one with the largest order. In this paper we study IHS manifolds of K3[2]-type with a symplectic action of Z34:A6 which also admit a non-symplectic automorphism. We characterize such IHS manifolds and prove their existence. We also prove that the order of a finite group acting on an IHS manifold of K3[2]-type is bounded by 174960, this bound is sharp and there is a unique IHS manifold of K3[2]-type acted by a group of this order, which is the Fano variety of lines of the Fermat cubic fourfold.

Funding Statement

The first and second authors have been partially supported by Fondecyt Iniciación en la Investigación N.11190428, while the first and third authors have been partially supported by Fondecyt Regular N.1240360. The third author has been supported by ANID Becas-Doctorado Nacional N.21191367. This work was started when the third author visited the Université de Poitiers; authors have been partially supported by Programa de cooperación científica ECOS-ANID C19E06 and Math AmSud-ANID 21 Math 02.

Citation

Download Citation

Paola COMPARIN. Romain DEMELLE. Pablo QUEZADA MORA. "Irreducible holomorphic symplectic manifolds with an action of ." J. Math. Soc. Japan Advance Publication 1 - 19, January, 2025. https://doi.org/10.2969/jmsj/93409340

Information

Received: 19 April 2024; Published: January, 2025
First available in Project Euclid: 8 January 2025

Digital Object Identifier: 10.2969/jmsj/93409340

Subjects:
Primary: 53C26
Secondary: 14C05 , 14J50

Keywords: automorphism group , hyperkähler manifolds , symplectic action

Rights: Copyright ©2025 Mathematical Society of Japan

Advance Publication
Back to Top