Título: Extremal divisors from the strata of abelian differentials.

Fecha y Hora: Viernes 24 de marzo de 2017 a las 12pm.

Lugar: Salón de seminarios, IMUNAM-Oaxaca.

Resumen: 

An abelian differential defines a flat metric with singularities at its zeros and poles, such that the underlying Riemann surface can be realised as a polygon whose edges are identified pairwise via translation. A number of questions about geometry and dynamics on Riemann surfaces reduce to studying the strata of abelian differentials with prescribed number and multiplicities of zeros and poles. In this talk we will focus on the divisorial strata closures that form special codimension-one subvarieties in the the Deligne-Mumford compactified moduli space of Riemann surfaces. For genus g>1 curves with n>g marked points, we show that infinitely many of these divisors form extremal rays of the cone of effective divisors. Hence these effective cones are not rational polyhedral.