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Trisecant lines and jacobians, II

Published online by Cambridge University Press:  04 December 2007

Olivier DEBARRE
Olivier DEBARRE
Affiliation:
Université Louis Pasteur, Department de Mathematiques, 7, Rue Rene Descartes, 67084, Strasbourg Cedex, France; e-mail: debarre@math.u-strasbg.fr
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Abstract

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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 $X$.

Keywords

complex abelain varietyJacobiantrisecantSchottky problem
Type
Research Article
Information
Compositio Mathematica , Volume 107 , Issue 2 , June 1997 , pp. 177 - 186
Copyright
© 1997 Kluwer Academic Publishers