Stability of tautological vector bundles on Hilbert squares of surfaces

TL;DR

This paper proves the stability of rank two tautological bundles on the Hilbert square of a surface under certain conditions and calculates their Chern classes, advancing understanding of their geometric properties.

Contribution

It establishes the stability of tautological bundles on Hilbert squares of surfaces and computes their Chern classes, providing new insights into their geometric structure.

Findings

Proved stability of rank two tautological bundles under mild positivity conditions.

Computed the Chern classes of these tautological bundles.

Enhanced understanding of their geometric and topological properties.

Abstract

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes.