Rank two nilpotent co-Higgs sheaves on complex surfaces

Abstract

Let $(\mathcal{E},\varphi )$ be a rank two co-Higgs vector bundles on a Kähler compact surface $X$ with $\varphi \in H^0(X,End(\mathcal{E})\otimes T_X)$ nilpotent. If $(\mathcal{E},\varphi )$ is semi-stable, then one of the following holds up to finite \' etale cover: $i)$ $X$ is uniruled. $ii)$ $X$ is a torus and $(\mathcal{E},\varphi )$ is strictly semi-stable. $iii)$ $X$ is a properly elliptic surface and $(\mathcal{E},\varphi )$ is strictly semi-stable.

Major changes, following suggestions of the referee

References in corpus (2)

• Generalized holomorphic bundles and the B-field action
• Constructing co-Higgs bundles on CP^2

Cited by in corpus (3)

• A vanishing theorem for co-Higgs bundles on the moduli space of bundles
• Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces
• Rational Morita equivalence for holomorphic Poisson modules