Torsion exceptional sheaves on weak del Pezzo surfaces of Type A

TL;DR

This paper studies torsion exceptional sheaves on certain weak del Pezzo surfaces, showing they can be constructed from line bundles on (-1)-curves using spherical twist functors, advancing understanding of their structure.

Contribution

It provides a method to generate all torsion exceptional sheaves on these surfaces via spherical twist functors from line bundles on (-1)-curves.

Findings

All torsion exceptional sheaves are obtainable from line bundles on (-1)-curves.

The construction involves successive spherical twist functors.

The work applies to weak del Pezzo surfaces with specific singularities.

Abstract

We investigate torsion exceptional sheaves on a weak del Pezzo surface of degree greater than two whose anticanonical model has at most $A_n$-singularities. We show that every torsion exceptional sheaf can be obtained from a line bundle on a $(-1)$-curve by acting spherical twist functors successively.