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The k - Very Ampleness and k - Spannedness on Polarized Abelian Surfaces

✍ Scribed by Hiroyuki Terakawa

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 676 KB
Volume: 195
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19981950113

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✦ Synopsis

We give a numerical criterion for an ample line bundle on an abelian surface to be k-very ample for a nonnegative integer k. This result implies the equivalence of k-very ampleness and k-spannedness. We also give a complete classification of polarized abelian surfaces with k-very ample polarizations. Our results extend those of BAUER and SZEMBERG [BaSzl] and RAMANAN [Ra].

and particularly it is an embedding if and only if L is (k + 1)-very ample (see (CG]).

On the other hand, BELTRAMETT~, FRANCIA and SOMMESE call L k-spanned if, for any curvilinear 0-dimensional subscheme (2, U Z ) of S with length(Oz) = k + 1,

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