29 nov 2018 -- 14:30
Aula 211, Dip. Matematica, Università "Roma Tre", Roma
Abstract.
When $X$ is a projective manifold and $\omega$ is a rational ample class, modular compactifications of the moduli space of stable vector bundles on $X$ have been constructed in Algebraic Geometry by putting appropriate classes of semistable sheaves at the boundary. These compactifications appear as global quotients. No similar constructions are known over a general compact Kaehler manifold $(X,\omega)$. In this talk we present an alternative construction method using "local quotients" which covers the case when $\omega$ is an arbitrary Kaehler class on a projective manifold $X$. This is the subject of joint recent work with Daniel Greb. Essential use is made of the notion introduced by Jarod Alper of a good moduli space of an algebraic stack. Besides solving a wall-crossing issue appearing in the context of projective manifolds, this alternative construction method is likely to extend to the general case of Kaehler manifolds.