Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Comparison of Poisson structures on moduli spaces

Let $X$ be a complex irreducible smooth projective curve, and let $L$ be an algebraic line bundle on $X$ with a nonzero section $\sigma$. Let $N$ denote the moduli space of stable Hitchin pairs $(E, \theta)$, where $E$ is an algebraic vector bundle on $X$ of fixed rank $r$ and degree $\delta$, and $\theta \in H^0(X, End(E)\otimes K_X\otimes L)$. Associating to every stable Hitchin pair its spectral data, an isomorphism of $N$ with a moduli space $M$ of stable sheaves of pure dimension one on the total space of $K_X\otimes L$ is obtained. Both the moduli spaces $M$ and $N$ are equipped with algebraic Poisson structures, which are constructed using $\sigma$. Here we prove that the above isomorphism between $M$ and $N$ preserves the Poisson structures. This is done together with Tomas Gomez and Francesco Bottacin