The Kuranishi map for vector bundles on certain products of curves

TL;DR

This paper investigates the deformation theory of vector bundles on product surfaces of curves, explicitly describing the Kuranishi map near unstable bundles and comparing the homologies of stable and unstable deformation spaces.

Contribution

It provides an explicit description of the Kuranishi map for vector bundles on product of curves and compares the homologies of stable and unstable deformation spaces.

Findings

Explicit description of the Kuranishi map near unstable bundles

Comparison of homologies of stable and unstable deformation spaces

Insights into the deformation theory of vector bundles on product surfaces

Abstract

We describe deformations of vector bundles on surfaces that are a product of two smooth projective curves. We explicitly describe the Kuranishi map around unstable vector bundles and compare the homologies of the Kuranishi spaces of stable and unstable deformations.