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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Noncomplete linear systems on abelian varieties
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by Christina Birkenhake PDF
Trans. Amer. Math. Soc. 348 (1996), 1885-1908 Request permission

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
  • © Copyright 1996 American Mathematical Society
  • 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