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1 results

  • Trisecant lines and jacobians, II

  • Olivier DEBARRE
  • Journal:
    Compositio Mathematica / Volume 107 / Issue 2 / June 1997
    Published online by Cambridge University Press:
    04 December 2007, pp. 177-186
    Print publication:
    June 1997
    • Article
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  • We prove that an indecomposable principally polarized complex abelian variety $X$ is the Jacobian of a smooth curve if and only if there exist points $a, b, c$of $X$ whose images under the Kummer map $X \rightarrow |2\Theta|^{\ast}$ are distinct and collinear, and such that the subgroup of X generated by $a - b$ and $b - c$ is dense in $X$.