A Kirwan blow-up and trees of vector bundles

TL;DR

This paper explicitly describes a Kirwan blow-up related to the compactification of moduli spaces of stable vector bundles on the projective plane, focusing on boundary components involving trees of surfaces.

Contribution

It provides a detailed construction of a Kirwan blow-up for the moduli space compactification on the projective plane, extending previous conceptual descriptions.

Findings

Explicit construction of Kirwan blow-up for the projective plane

Description of boundary components involving trees of surfaces

Enhanced understanding of moduli space compactifications

Abstract

In the paper [MTT] a conceptuel description of compactifications of moduli spaces of stable vector bundles on surfaces has been given, whose boundaries consist of vector bundles on trees of sufaces. In this article a typical basic case for the projective plane is described explicitly including the constrution of a relevant Kirwan blow up.