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arXiv · 0912.4615

On moduli spaces of Hitchin pairs

Indranil Biswas·Peter B. Gothen·Marina Logares
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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 $(E ,ϕ\in H^0(End(E)\otimes L))$ 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 $X$.

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Indranil Biswas, Peter B. Gothen, Marina Logares. 2011-04-15. On moduli spaces of Hitchin pairs. https://doi.org/10.1017/s0305004111000405

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