# Existence of nontrivial logarithmic co-Higgs structure on curves

## TL;DR

This paper investigates the existence, properties, and parameter spaces of nontrivial logarithmic co-Higgs structures on unstable bundles over algebraic curves, extending some results to higher dimensions.

## Contribution

It provides criteria for the existence and non-existence of such structures, describes their parameter spaces, and explores their invariants and higher-dimensional cases.

## Key findings

- Criteria for existence and non-existence established
- Parameter spaces of structures described
- Higher-dimensional cases analyzed

## Abstract

We study various aspects on nontrivial logarithmic co-Higgs structure associated to unstable bundles on algebraic curves. We check several criteria for (non-)existence of nontrivial logarithmic co-Higgs structures and describe their parameter spaces. We also investigate the Segre invariants of these structures and see their non-simplicity. In the end we also study the higher dimensional case, specially when the tangent bundle is not semistable.