Prym varieties and the Schottky problem

  title={Prym varieties and the Schottky problem},
  author={Arnaud Beauville},
  journal={Inventiones mathematicae},
  • A. Beauville
  • Published 1 June 1977
  • Mathematics
  • Inventiones mathematicae
be the moduli space of principally polarized abelian varieties of dimension g, Jg c ~q/g the locus of Jacobians. The problem is to find explicit equations for Jg (or rather its closure Jg) in s/g. In their beautiful paper [A-M], Andreotti and Mayer prove that Jg is an irreducible component of the locus N~_ 4 of principally polarized abelian varieties (A, O) with dim Sing O > g 4 . Then they give a procedure to write "explicit" equations for N~_ 4. There is no hope that Jg be equal to Ng_ 4… 
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