Higher-dimensional O'Grady's resolutions and their exceptional locus

Luigi Martinelli

Higher-dimensional O'Grady's resolutions and their exceptional locus

Algebraic Geometry 2025-07-25 v2

Authors: Luigi Martinelli

Abstract

For any $n \ge 3$ , we consider the moduli space $M_n$ of semistable sheaves with Mukai vector $2(1,0,1-n)$ on a K3 surface. The moduli space $M_n$ is singular and lacks a crepant resolution, but might still admit a categorical crepant one. As a preliminary to exploring this possibility, we study the explicit resolution of singularities of $M_n$ constructed by O'Grady, and provide a global description of its exceptional locus.

Keywords

moduli spaces of sheaves crepant resolution conjecture moduli spaces

Cite

@article{arxiv.2502.20094,
  title  = {Higher-dimensional O'Grady's resolutions and their exceptional locus},
  author = {Luigi Martinelli},
  journal= {arXiv preprint arXiv:2502.20094},
  year   = {2025}
}

Comments

Section 2 rewritten. Minor corrections and improved exposition in the other sections. Added references

Higher-dimensional O'Grady's resolutions and their exceptional locus

Abstract

Keywords

Cite

Comments

Related papers