A note on Abelian varieties embedded in quadrics

Details A note on Abelian varieties embedded in quadrics A note on Abelian varieties embedded in quadrics

2003-04-29

arxiv.org/abs/math/0304479v2

Mathematics

Algebraic Geometry

5 pages

Scientific paper

We show that if A is a d-dimensional abelian variety in a smooth quadric of
dimension 2d then d=1 and A is an elliptic curve of bidegree (2,2) on a
quadric. This extends a result of Van de Ven which says that A only can be
embedded in P^{2d} when d=1 or 2.

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