Buser-Sarnak invariant and projective normality of abelian varieties

Details Buser-Sarnak invariant and projective normality of abelian varieties Buser-Sarnak invariant and projective normality of abelian varieties

2010-03-03

arxiv.org/abs/1003.0742v1

Mathematics

Algebraic Geometry

to appear in the Proceedings of CDG2009 (Hannover)

Scientific paper

We show that a general $n$-dimensional polarized abelian variety $(A,L)$ of a given polarization type and satisfying $ h^0(A, L) \geq \dfrac{8^n}{2} \cdot \dfrac{n^n}{n !}$ is projectively normal. In the process, we also obtain a sharp lower bound for the volume of a purely one-dimensional complex analytic subvariety in a geodesic tubular neighborhood of a subtorus of a compact complex torus.

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