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Abstract: In this survey we discuss some of the classical and modern methods instudying the Riemann-Schottky problem, the problem of characterizingJacobians of curves among principally polarized abelian varieties. We presentmany of the recent results in this subject, and describe some directions ofcurrent research. This paper is based on the talk given at the -Classicalalgebraic geometry today- workshop at MSRI in January 2009.

Author: Samuel Grushevsky


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