Compact Moduli of Algebraic Varieties

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

The award supports research in algebraic geometry, a central branch of mathematics which aims to understand, both practically and conceptually, solutions of systems of polynomial equations in many variables. Algebraic geometry has important applications to other fields of mathematics, such as number theory, topology, and analysis, as well as to physics, biology, cryptography, and engineering. Young researchers including graduate students will be involved in this project. The PI will work on a variety of topics centered around degenerations of algebraic varieties and functorial, geometrically meaningful compactifications of their moduli spaces. The central part of the project is the study of functorial compactifications of moduli spaces of K-trivial varieties, such as K3 surfaces, hyperkahler varieties, Calabi-Yau varieties, and abelian varieties, including both explicit descriptions of these compactifications, as well as their properties such as Kodaira dimension and canonical models. A separate project is on the volumes of log surfaces. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.