Compact Moduli and K-stability of Fano Varieties

Speaker's Name: Joseph Malbon
Speaker's Affiliation: University of Edinburgh
Speaker's Research Theme(s): Pure Mathematics
Abstract:
Fano varieties are a class of varieties of fundamental importance in algebraic geometry. Studied since the early beginnings of the subject, they are now known to be building blocks from which all varieties are constructed. A key part of the classification of algebraic varieties concerns the construction and description of moduli spaces. However, in contrast to the general-type case, moduli spaces for Fano varieties have historically been difficult to construct. K-stability is a notion originating in differential geometry, providing an algebro-geometric criterion for the existence of certain canonical metrics. Since its introduction into algebraic geometry, it has also been accepted as the correct moduli theory for Fano varieties, guaranteeing many desirable properties such as separatedness and compactness. In this talk, we will give a friendly introduction to the subject of moduli and K-stability, and provide a concrete description of the K-moduli space for a certain family of Fano threefolds.

Venue: Maths A17