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The k ‐ Very Ampleness and k ‐ Spannedness on Polarized Abelian Surfaces
Author(s) -
Terakawa Hiroyuki
Publication year - 1998
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19981950113
Subject(s) - mathematics , abelian group , ample line bundle , equivalence (formal languages) , integer (computer science) , pure mathematics , combinatorics , computer science , programming language
We give a numerical criterion for an ample line bundle on an abelian surface to be it‐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].