Giovanni Inchiostro (UW)

PDL C-38

Title pretalk: Moduli spaces and Kontsevich stable maps

Abstract pretalk: During this pretalk I will talk about moduli spaces, with a special emphasis on moduli spaces of Kontsevich-stable maps.

Title talk: Degenerations of twisted maps to algebraic stacks

Abstract talk: Assume that one has a family of nodal curves over the punctured disc , with a morphism to an algebraic stack with a projective good moduli space. I will explain how one can, up to replacing the punctured disc with a ramified cover of it, compactify this family to a family of nodal (twisted) curves over the whole disc , in a way such that the generic morphism extends to .

For example, in the case where , this gives a recipe to extend fibrations in Brauer-Severi varieties, whereas for this gives a way to extend families of line bundles with a section. The talk is based on a joint work with Andrea Di Lorenzo.