Structure of Functorial Compactification of Moduli of Abelian Varieties and their Relatives

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

Structure of functorial compactification of moduli of abelian varieties and their relatives The investigator will continue to study the moduli of stable pairs with semiabelian group action and, in particular, the part which gives the functorial compactification of the moduli of abelian varieties. The aims are: to get a detailed description of the structure of this space and the way the closure of the Schottky locus sits inside of it; to study generalizations of this moduli space to the relative case and to the case of other group actions. The methods employed are going to be both algebro-geometric and combinatorial. This research is in the field of algebraic geometry, but with a strong combinatorial aspect. The main object of algebraic geometry is solutions of polynomial equations. Started in the ancient times, in the 20th century it saw development of new and enormously powerful methods. Its applications reach across the scientific boundaries to such diverse fields as physics and cryptography. Combinatorics concerns counting, and is the basis of most real-life applications of mathematics. The grant will also support education and scientific training of new PhD students.