Algebraic and Arithmetic Geometry Seminar

Surfaces with close to irrational Seshadri constants

by Sönke Rollenske (Universität Marburg)

Aula Seminari (Dipartimento di Matematica)

Aula Seminari

Dipartimento di Matematica


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.