Giovanni Inchiostro (UW)
Tuesday, May 30, 2023 - 2:30pm
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 
.
, 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 
![\mathcal{M} = [\mathbb{A}^1/\mathbb{G}_m]](https://ci3.googleusercontent.com/proxy/3HhT7yxVaple_0vfrmXtSZvqXHhS4y8JiVtzbbcWgw5HA7SodMQ4L5SCYZLNAZb29BB6njSxE-FFAZWOeY_OCGWwUXX4gWF3Zia7coN6_QNywpl2F6ckoITNJb5MtF4p5AZIRtiniEPGGgNjio8jDxVuOihnE4B9V8vLYjXC115FzEFUB31q4cYlPP1YAKFVRMdgSIe6Ax4=s0-d-e1-ft#https://s0.wp.com/latex.php?zoom=3&bg=ffffff&fg=000000&s=0&latex=%5Cmathcal%7BM%7D%09=%09[%5Cmathbb%7BA%7D%5E1/%5Cmathbb%7BG%7D%5Fm] "\mathcal{M} = [\mathbb{A}^1/\mathbb{G}_m]")