Spherical vector bundles on nodal K3 surfaces

TL;DR

This paper investigates how the presence of a node on a K3 surface affects the existence of stable spherical sheaves, revealing potential obstructions related to Chern classes.

Contribution

It demonstrates that nodal degenerations of K3 surfaces can obstruct the existence of certain stable spherical sheaves, highlighting new geometric constraints.

Findings

Obstructions to stable spherical sheaves on nodal K3 surfaces.

Dependence of sheaf existence on Chern classes.

Insights into the geometry of singular K3 surfaces.

Abstract

We show that when a K3 surface acquires a node, the existence of stable spherical sheaves of certain Chern classes can be obstructed.