English

Cubic surfaces and cubic threefolds, jacobians and intermediate jacobians

Algebraic Geometry 2007-05-23 v3 Complex Variables

Abstract

In this paper we study principally polarized complex abelian varieties that admit an automorphism of order 3. It turns out that certain natural conditions on the multiplicities of its action on the differentials of the first kind do guarantee that those polarized varieties are not jacobians of curves. As an application, we get another proof of the already known (thanks to Clemens and Griffiths) fact that intermediate jacobians of certain cubic threefolds are not jacobians of curves.

Keywords

Cite

@article{arxiv.math/0610138,
  title  = {Cubic surfaces and cubic threefolds, jacobians and intermediate jacobians},
  author = {Yuri G. Zarhin},
  journal= {arXiv preprint arXiv:math/0610138},
  year   = {2007}
}

Comments

LaTeX, 4 pages

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