Non-locally-free locus of O'Grady's ten dimensional example

TL;DR

This paper provides an explicit description of the fibers of a birational morphism related to O'Grady's ten-dimensional moduli space of sheaves on a K3 surface, enhancing understanding of its geometric structure.

Contribution

It offers a detailed, explicit characterization of the fibers of the birational morphism in O'Grady's ten-dimensional example, which was previously not fully described.

Findings

Explicit description of fibers of the birational morphism

Enhanced understanding of the moduli space's geometric structure

Clarification of the relationship between the moduli space and Donaldson-Uhlenbeck compactification

Abstract

We give a completely explicit description of the fibers of the natural birational morphism from O'Grady's ten dimensional singular moduli space of sheaves on a K3 surface to the corresponding Donaldson-Uhlenbeck compactification.