Three Applications of Instanton Numbers

TL;DR

This paper explores the use of instanton numbers in three different mathematical applications: classifying vector bundles, computing homology of moduli spaces, and differentiating curve singularities.

Contribution

It introduces novel methods leveraging instanton numbers for stratification, homology calculation, and singularity distinction in algebraic geometry.

Findings

Instanton numbers effectively stratify moduli of vector bundles.

They enable calculation of relative homology in moduli spaces.

They distinguish different types of curve singularities.

Abstract

We use instanton numbers to: (i) stratify moduli of vector bundles, (ii) calculate relative homology of moduli spaces and (iii) distinguish curve singularities.