Known one- and two-loop superstring chiral measures are restated as path integrals of the Gelca-Hamilton 3D TQFT over handlebodies, with modular transformations interpreted as bulk mapping class group moves.
The Schottky Problem
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In this survey we discuss some of the classical and modern methods in studying the (Riemann-)Schottky problem, the problem of characterizing Jacobians of curves among principally polarized abelian varieties. We present many of the recent results in this subject, and describe some directions of current research. This paper is based on the talk given at the "Classical algebraic geometry today" workshop at MSRI in January 2009.
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Genus 2 Superstring Chiral Measure From The 3-Dimensional Gelca-Hamilton TQFT
Known one- and two-loop superstring chiral measures are restated as path integrals of the Gelca-Hamilton 3D TQFT over handlebodies, with modular transformations interpreted as bulk mapping class group moves.