Blowups of surfaces and moduli of holomorphic vector bundles

TL;DR

This paper investigates the moduli space of framed holomorphic bundles on the blowup of a complex surface, focusing on a filtration related to the bundles' behavior near the exceptional divisor.

Contribution

It introduces a new filtration method to analyze the moduli of holomorphic bundles on blown-up surfaces, enhancing understanding of their structure.

Findings

Characterization of the filtration induced by the exceptional divisor

Insights into the structure of the moduli space of bundles on blowups

Potential applications to classification problems in complex geometry

Abstract

We examine the moduli of framed holomorphic bundles over the blowup of a complex surface, by studying a filtration induced by the behavior of the bundles on a neighborhood of the exceptional divisor.