On Seshadri constants

Abstract: The Seshadri constant of a polarized variety $(X,L)$ at a point $x$ measures how positive is the polarization $L$ at $x$. If $x$ is very general, the Seshadri constant does not depend on $x$, and captures global information on $X$. Inspired by ideas from the Geometry of Numbers, we introduce in this talk successive Seshadri minima, such that the first one is the Seshadri constant at a point, and the last one is the width of the polarization at the point. Assuming the point is very general, we obtain two results: a) the product of the successive Seshadri minima is proportional to the volume of the polarization; b) if $X$ is toric, the $i$-th successive Seshadri constant is proportional to the $i$-th successive minima of a suitable $0$-symmetric convex body. Based on joint work with Atsushi Ito.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

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