Mike Roth (Queen's University)

Algebra & Geometry Seminar

Speaker: Mike Roth (Queen's University)

Title: An irrational Seshadri constant, after Laface and Ugaglia

Abstract: This talk will give an overview of the ideas surrounding a recent breakthrough preprint (September 22, 2026), establishing the first example of a Seshadri constant which is known to be irrational. The question of ‘irrational Seshadri constants’ in its most general form has been open for more than 20 years, while the most famous specific case, the Nagata conjecture, has been open for 68 years.

The recent preprint does not answer the ‘Nagata question’, but it is close, in the sense that one of the examples is an irrational Seshadri constant on P^2 blown up at 10 points, the first setting where the Nagata conjecture applies.

The first example produced in the paper is an irrational Seshadri constant on P^1 x P^1 blown up at 10 points, using an approach suggested in a paper of Dionne and Roth. The authors then use this example and, by passing to a quotient by a finite group action, are able to produce an example on P^2.