Moduli Spaces of Toric and Abelian Pairs

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Alexeev9870062In this project, Alexeev will continue investigating the canonical functorial compactification of the moduli space of principally polarized varieties, and similar moduli spaces of toric and semiabelian pairs. This is research in the field of algebraic geometry. Algebraic geometry is one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.