Moduli spaces of polarised symplectic O'Grady varieties and Borcherds products

TL;DR

This paper investigates the moduli spaces of ten-dimensional O'Grady symplectic varieties, revealing their structure as covers of 21-dimensional modular varieties with novel arithmetic groups, distinct from K3 cases.

Contribution

It introduces the study of moduli spaces for O'Grady's ten-dimensional varieties with a focus on their relation to higher-dimensional modular varieties and unique arithmetic groups.

Findings

Moduli spaces are covers of 21-dimensional modular varieties.

The arithmetic group involved is larger than the stable orthogonal group.

Distinct from K3 and K3^[n] cases in dimension and group structure.

Abstract

We study moduli spaces of O'Grady's ten-dimensional irreducible symplectic manifolds. These moduli spaces are covers of modular varieties of dimension 21, namely quotients of hermitian symmetric domains by a suitable arithmetic group. The interesting and new aspect of this case is that the group in question is strictly bigger than the stable orthogonal group. This makes it different from both the K3 and the K3^[n] case, which are of dimension 19 and 20 respectively.