Very ample linear systems on abelian varieties

1993/06/04 by Olivier Debarre, O. Debarre, Debarre, O. +6
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Tensor decomposition and applications #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9306004

29 pages, typeset with AMS-LaTeX 1.1

arxiv created 1993/06/04 · arxiv updated 2009/11/30

Abstract

Let (X,L) be a polarized complex abelian variety of dimension g where L is a polarization of type (1,...,1,d). For (X,L) genberic we prove the following: (1) If d ≥ g+2, then ϕ_L\colon X → \bf P^d-1 defines a birational morphism onto its image. (2) If d > 2^g, then L is very ample. We show the latter by checking it on a suitable rank-(g-1)-degeneration.

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