On moduli spaces of Hitchin pairs

Details On moduli spaces of Hitchin pairs On moduli spaces of Hitchin pairs

2009-12-23

arxiv.org/abs/0912.4615v2

Mathematics

Algebraic Geometry

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

Scientific paper

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 $(E ,\phi\in H^0(End(E)\otimes L))$ 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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