Annual Seminar for Mathematics Research Scholars
Speaker: Cyril J Jacob, CMI
Date: Thursday, 05 October 2023
Time: 11 AM
Venue: Lecture Hall 801
Lower bounds for Seshadri constants on general blow-ups of P^2
Cyril J Jacob
Chennai Mathematical Institute.
05-10-23

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Abstract

Seshadri constants of ample line bundles can be arbitrarily small for blow-ups of points in P^2 by an example of Miranda. This raises a question: Is there any surface where the infimum of Seshadri constants of all ample line bundles at all points is zero? In this talk, we will show assuming a generalized SHGH conjecture (proposed by Farnik, Hanumanthu, Huizenga, Schmitz, and Szemberg in 2020 ), this can not happen on a general blow-up of P^2. More precisely, we will show conjecturally that Seshadri constant at any point in the general blow-up of P^2 for any ample line bundle is at least 1. This is also a generalization of the result by Ein-Lazarfeld for Seshadri constants of ample line bundles at a very general point on an arbitrary surface.