A vanishing theorem for co-Higgs bundles on the moduli space of bundles

Abstract

We consider smooth moduli spaces of semistable vector bundles of fixed rank and determinant on a compact Riemann surface $X$ of genus at least $3$. The choice of a Poincaré bundle for such a moduli space $M$ induces an isomorphism between $X$ and a component of the moduli space of semistable sheaves over $M$. We prove that $h^0(M,\text{End}(\mathcal{E})\otimes TM)=1$ for a vector bundle $\mathcal{E}$ on $M$ coming from this component. Furthermore, there are no nonzero integrable co-Higgs fields on $\mathcal{E}$.

Final version

References in corpus (3)

• Generalized holomorphic bundles and the B-field action
• Constructing co-Higgs bundles on CP^2
• Rank two nilpotent co-Higgs sheaves on complex surfaces

Cited by in corpus (3)

• Homogeneous Higgs and co-Higgs bundles on Hermitian symmetric spaces
• Toric co-Higgs bundles on toric varieties
• Rational Morita equivalence for holomorphic Poisson modules