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Published in:
2011 | OriginalPaper | Chapter
Buser-Sarnak invariant and projective normality of abelian varieties
Authors : Jun-Muk Hwang, Wing-Keung To
Published in: Complex and Differential Geometry
Publisher: Springer Berlin Heidelberg
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We show that a general n-dimensional polarized abelian variety
(A,L)
of a given polarization type and satisfying
$$h^0(A,L)\geq \frac{8^n}{2}. \frac{n^n}{n !}$$
is projectively normal. In the process, we also obtain a sharp lower bound for the volume of a purely onedimensional complex analytic subvariety in a geodesic tubular neighborhood of a subtorus of a compact complex torus.