Commutative Algebra Seminar
Eric Canton
University of Michigan
K-stability and Free Resolutions
Abstract: K-stability is concerned with one parameter families of a fixed projective variety that are generated by a one-dimensional torus action; stated more algebraically, Grobner degenerations of the homogenous ideals defining the variety under various embeddings. This has been re-interpreted in recent years in terms of singularities of pairs arising in the minimal model program, having implications for certain moduli spaces. These connections are surprising and intriguing, given that Tian (and Donaldson) defined K-stability complex-analytically (and algebraically, respectively) to study the question of existence of Kahler-Einstein metrics on smooth Fano varieties. Many results require techniques from complex differential geometry, the minimal model program, or non-Archimedean geometry. In this talk, I'll give some background on this topic and a flavor of ongoing work studying K-stability via free resolutions.
Monday April 29, 2019 at 4:00 PM in 427 SEO