Geometry Seminar

University of Tor Vergata, Department of Mathematics

25th of October 2022, 14:30-15:30, room “Dal Passo”

Speaker

Francesca Carocci

(EPFL)

Title

Smooth compactifications of moduli of low genus curves in projective spaces via log geometry and Gorenstein singularities

Abstract

Moduli spaces of stable maps in higher genus have many components of different dimensions meeting each other in complicated ways, and the closure of the smooth locus (the so called main component) does not have a modular interpretation. Constructing modular desingularisations of the main component is strictly related to understanding degenerations of canonical divisors and  Gorenstein singularities.

I will explain how logarithmic and tropical techniques can be used to solve the problem in genus one and two and say a few words on how the methods used  can be adapted to construct modular binational models of pointed curves in low genus.

This is based on a joint work with L.Battistella