On the Harder-Narasimhan filtration of the direct image of the structure sheaf

TL;DR

This paper computes the Harder-Narasimhan filtration of vector bundles arising from the direct image of the structure sheaf under certain finite morphisms.

Contribution

It provides explicit calculations of the Harder-Narasimhan filtration for specific classes of finite morphisms, advancing understanding of vector bundle stability.

Findings

Computed the Harder-Narasimhan filtration for certain finite morphisms.

Identified cases where the filtration can be explicitly described.

Enhanced understanding of the stability properties of direct image sheaves.

Abstract

We compute the Harder-Narasimhan filtration of vector bundles $f_*\mathcal O_Y$ for certain finite morphisms $f\,:\,Y\,\longrightarrow\, X$ and in some other cases.