K-moduli of quasimaps and quasi-projectivity of K-stable Calabi-Yau fibrations over curves
Masafumi Hattori (University of Nottingham)
Tuesday 3rd June 15:00-16:00
Maths 311B
Abstract
K-stability is an important notion in algebraic geometry, which is introduced to detect the existence of constant scalar curvature Kahler metrics, as the Yau-Tian-Donaldson conjecture predicted. On the other hand, this notion is also closely related to GIT and moduli theory. Odaka predicted that we can construct a moduli space (K-moduli) by using K-stability and Xu et. al. constructed K-moduli theory for log Fano pairs with an ample CM line bundle, which is a line bundle canonically defined. However, Odaka’s K-moduli conjecture is still open for general polarized varieties.
In this talk, we introduce uniform adiabatic K-stability for Calabi-Yau fibrations, that is a uniform notion of K-stability when the polarization is very close to the base line bundle, and we construct K-moduli theory of Calabi-Yau fibrations over curves. Moreover, we will construct K-moduli theory for log Fano quasimaps and apply it to the quasi-projectivity for K-moduli of Calabi-Yau fibrations.
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