Logarithmic co-Higgs bundles

TL;DR

This paper introduces logarithmic co-Higgs sheaves on projective manifolds, proves their existence with nilpotent fields, and explores related moduli problems, especially over algebraic curves of low genus.

Contribution

It defines logarithmic co-Higgs sheaves, establishes their existence with nilpotent fields, and studies associated moduli problems on algebraic curves.

Findings

Existence of logarithmic co-Higgs sheaves with nilpotent fields

Construction of moduli spaces for these sheaves

Application to algebraic curves of low genus

Abstract

In this article we introduce a notion of logarithmic co-Higgs sheaves associated to a simple normal crossing divisor on a projective manifold, and show their existence with nilpotent co-Higgs fields for fixed ranks and second Chern classes. Then we deal with various moduli problems with logarithmic co-Higgs sheaves involved, such as coherent systems and holomorphic triples, specially over algebraic curves of low genus.