The moduli continuity method for log Fano pairs

21-May-2020, 12:30-13:30 (4 years ago)

Abstract: The moduli continuity method, pioneered by Odaka, Spotti and Sun, allows us to explicitly provide algebraic charts of the Gromov-Hausdorff compactification of (possibly singular) Kähler-Einstein metrics. Assuming we can provide a homeomorphism to some 'known' algebraic compactification (customarily, a GIT one) the method allows us to determine which Fano varieties (or more generally log Fano pairs) are K-polystable in a given deformation family. In this talk we provide the first examples of compactification of the moduli of log Fano pairs for the simplest deformation family: that of projective space and a hypersurface, and mention related results for cubic surfaces. This is joint work with Patricio Gallardo and Cristiano Spotti.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


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.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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