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Higher order embeddings of algebraic surfaces of Kodaira dimension zero

Higher order embeddings of algebraic surfaces of Kodaira dimension zero Math. Z. 229, 417–433 (1998) c Springer-Verlag 1998 Higher order embeddings of algebraic surfaces of Kodaira dimension zero Hiroyuki Terakawa Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-50, Japan Received January 20, 1997; in final form May 21, 1997 1. Introduction Let L be a line bundle on a smooth connected projective surface S over the complex number field C. L is said to be k-very ample (resp. k-spanned) for an integer k  0 if, given any (resp. curvilinear) 0-cycle (Z; O ) of S with length(O )= k +1, the restriction map Γ (L) ! Γ (O (L)) is Z Z surjective. Note that L is 0-very ample if and only if L is generated by its global sections, and L is 1-very ample if and only if L is very ample. For k  2, L being k-very ample is equivalent to L being k-spanned ([B-F-S]). A k-very ample line bundle L gives naturally a ‘k-th order embedding’ [r] as follows. Let S be the Hilbert scheme of 0-dimensional subschemes of S of length r and let Grass(r; Γ (L)) be the Grassmannian of all r-dimensional quotients of Γ (L). Then http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Higher order embeddings of algebraic surfaces of Kodaira dimension zero

Terakawa, Hiroyuki
Mathematische Zeitschrift , Volume 229 (3) – Nov 1, 1998
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References (19)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Springer-Verlag Berlin Heidelberg
Subject
Legacy
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/PL00004664
Publisher site
See Article on Publisher Site

Abstract

Math. Z. 229, 417–433 (1998) c Springer-Verlag 1998 Higher order embeddings of algebraic surfaces of Kodaira dimension zero Hiroyuki Terakawa Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-50, Japan Received January 20, 1997; in final form May 21, 1997 1. Introduction Let L be a line bundle on a smooth connected projective surface S over the complex number field C. L is said to be k-very ample (resp. k-spanned) for an integer k  0 if, given any (resp. curvilinear) 0-cycle (Z; O ) of S with length(O )= k +1, the restriction map Γ (L) ! Γ (O (L)) is Z Z surjective. Note that L is 0-very ample if and only if L is generated by its global sections, and L is 1-very ample if and only if L is very ample. For k  2, L being k-very ample is equivalent to L being k-spanned ([B-F-S]). A k-very ample line bundle L gives naturally a ‘k-th order embedding’ [r] as follows. Let S be the Hilbert scheme of 0-dimensional subschemes of S of length r and let Grass(r; Γ (L)) be the Grassmannian of all r-dimensional quotients of Γ (L). Then

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Mathematische Zeitschrift – Springer Journals

Published: Nov 1, 1998

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