Exceptional sheaves on the Hirzebruch surface $\mathbb{F}_2$

TL;DR

This paper explores the classification of exceptional sheaves on the Hirzebruch surface _2, aiming to understand their structure and properties as part of broader efforts on weak del Pezzo surfaces.

Contribution

It provides initial classification results for exceptional sheaves on _2, advancing the understanding of exceptional objects on weak del Pezzo surfaces.

Findings

Identified specific classes of exceptional sheaves on _2

Established foundational properties for these sheaves

Paved the way for further classification on weak del Pezzo surfaces

Abstract

We investigate exceptional sheaves on the Hirzebruch surface $\mathbb{F}_2$, as the first attempt toward the classification of exceptional objects on weak del Pezzo surfaces.