The intersection cohomology of the moduli space of Higgs bundles on a smooth projective curve. (Camilla Felisetti, UniGe)

26.09.2018 14:30

Abstract: Let X be a smooth projective curve of genus g over $\mathbb{C}$. The character variety $\mathcal{M}_B$ parametrizing conjugacy classes of representations from the fundamental group of X into $SL(2,\mathbb{C})$ is an affine irreducible singular projective variety. The Non Abelian Hodge theorem states that there is a real analytic isomorphism between $\mathcal{M}_B$ and the quasi projective singular variety $\mathcal{M}_{Dol}$ which parametrizes semistable Higgs bundles of rank 2 and degree 0 on X.
During the seminar I will present a desingularization of these moduli spaces and I will compute the intersection cohomology of $\mathcal{M}_{Dol}$ using the famous Decomposition theorem by Beilinson, Bernstein, Deligne and Gabber. Moreover I will show that the mixed Hodge structure on the intersection cohomology is pure, showing evidence that an analogue of the P=W conjecture might hold for singular moduli spaces.

Lieu

Bâtiment: Villa Battelle

Séminaire de la Tortue

entrée libre