# Isomonodromic deformations and very stable vector bundles of rank two

## TL;DR

This paper proves that for a universal isomonodromic deformation of certain rank two connections on complex curves, the associated vector bundles are not only stable but also very stable, meaning they admit no nonzero nilpotent Higgs fields.

## Contribution

It establishes that the vector bundles arising from a general parameter in the universal deformation are very stable, extending previous stability results.

## Key findings

- Vector bundles are stable for general parameters.
- Vector bundles are very stable, with no nonzero nilpotent Higgs fields.
- Results apply to genus at least two curves.

## Abstract

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this universal deformation. In a previous work we proved that the vector bundle corresponding to a general parameter of this family is stable. Here we prove that the vector bundle corresponding to a general parameter is in fact very stable (it does not admit any nonzero nilpotent Higgs field).