Existence of nontrivial logarithmic co-Higgs structure on curves

2017/03/13 by Ballico, Edoardo, Huh, Sukmoon
#14D20 #14H60 #14J60 #53D18 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.04475

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.

Related

• Logarithmic co-Higgs bundles
• A note on co-Higgs bundles
• Three instability stratifications of the stack of Higgs bundles on a smooth projective curve
• Strong semistability of Higgs bundles over curves
• Relative Log-Symplectic structure on a semi-stable degeneration of moduli of Higgs bundles