Noncomplete linear systems on abelian varieties

Author:
Christina Birkenhake

Journal:
Trans. Amer. Math. Soc. **348** (1996), 1885-1908

MSC (1991):
Primary 14C20, 14K05

DOI:
https://doi.org/10.1090/S0002-9947-96-01570-X

MathSciNet review:
1340170

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Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a smooth projective variety. Every embedding $X\hookrightarrow \mathbb {P}_N$ is the linear projection of an embedding defined by a complete linear system. In this paper the geometry of such not necessarily complete embeddings is investigated in the special case of abelian varieites. To be more precise, the properties $N_p$ of complete embeddings are extended to arbitrary embeddings, and criteria for these properties to be satisfied are elaborated. These results are applied to abelian varieties. The main result is: *Let $(X,L)$ be a general polarized abelian variety of type $(d_1,\dots ,d_g)$ and $p\ge 1$, $n\ge 2p+2$ such that $nd_g\ge 6$ is even, and $c\le n^{g-1}$. The general subvector space $V\subseteq H^0(L^n)$ of codimension $c$ satisfies the property $N_p$.*

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Additional Information

**Christina Birkenhake**

Affiliation:
Mathematisches Institut, Universität Erlangen Bismarckstrasse 1$\frac 12$, D-91054 Erlangen, Germany

Email:
Birkenhake@mi.uni-erlangen.de

Received by editor(s):
June 9, 1995

Additional Notes:
Supported by EC Contract No. CHRXCT 940557

Article copyright:
© Copyright 1996
American Mathematical Society