Surfaces with close to irrational Seshadri constants.

Data Seminario: 
15-Sep-2021
Ora Inizio: 
15:00
Ora Fine: 
16:00
Sönke Rollenske
University of Marburg (Germany)

Gli interessati a seguire il seminario in presenza sono pregati di contattare il prof. Franciosi

ABSTRACT:
Surfaces with close to irrational Seshadri constants.
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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 $\epsilon (
\mathcal O_X(1), x)$ lies in the interval $\left[\sqrt{d}- \frac d m, \sqrt{d}
\right]$ and thus approaches the possibly irrational number $\sqrt d$ as $m$
grows ($d\geq 2$ and $m\geq 3$).

This is joint work with A. K\"uronya