Mathematics Research Institute


Global geometry of surfaces defined by non-positive at infinity valuations

Carlos Jesús Moreno Ávila (Universidad de Valladolid)

Fecha: 29/10/2021 12:00
Lugar: Seminario IMUVA. Edificio LUCIA.

In this talk we consider plane divisorial valuations of Hirzebruch surfaces and introduce the concept of non-positivity at infinity. We see that the surfaces given by valuations of the last types have nice global and local geometric properties. Moreover, non-positive at infinity divisorial valuations are those divisorial valuations of Hirzebruch surfaces providing rational surfaces with minimal generated cone of curves. Finally, we compute the Seshadri-type constants for pairs formed by a big divisor and a divisorial valuation of a Hirzebruch surface and obtain the vertices of the Newton-Okounkov bodies of pairs as above under the non-positivity at infinity property. This talk is based on a joint work with C. Galindo and F. Monserrat. Este es el segundo seminario de una serie de dos.