On moduli spaces of Hitchin pairs

Abstract

Let $X$ be a compact Riemann surface $X$ of genus at--least two. Fix a holomorphic line bundle $L$ over $X$. Let $\mathcal{M}$ be the moduli space of Hitchin pairs $(E,\varphi \in H^0(End(E)\otimes L))$ over $X$ of rank $r$ and fixed determinant of degree $d$. We prove that, for some numerical conditions, $\mathcal{M}$ is irreducible, and that the isomorphism class of the variety $\mathcal{M}$ uniquely determines the isomorphism class of the Riemann surface $X$.

18 pages; final version, accepted in Math. Proc. Cambridge Phil. Soc

References in corpus (3)

• Homological algebra of twisted quiver bundles
• Homotopy groups of moduli spaces of representations
• Torelli theorem for the moduli spaces of pairs

Cited by in corpus (6)

• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Twisted argyle quivers and Higgs bundles
• Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces
• Symplectic geometry of a moduli space of framed Higgs bundles
• Torelli theorem for moduli stacks of vector bundles and principal G-bundles
• Generalized Deligne-Hitchin Twistor Spaces: Construction and Properties