Algebraic and Arithmetic Geometry Seminar

# Surfaces with close to irrational Seshadri constants

## by Sönke Rollenske (Universität Marburg)

Europe/Rome
Aula Seminari (Dipartimento di Matematica)

### Aula Seminari

#### Dipartimento di Matematica

Description

Seshadri constants measure local positivity of line bundles and it is an open question if they can be irrational on algebraic surfaces. I will recall this concept and prove that for a general point on a general hypersurface of degree $md$ in $\mathbb{P}(1,1,1,m)$ the Seshadri constant $\epsilon (\mathcal{O}_X(1), x)$ approaches the possibly irrational number $\sqrt d$ as $m$ grows ($d >1$ and $m>2$). This is joint work with A. Küronya.