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On syzygies of Veronese embedding of arbitrary projective varieties
- Authors
- Park, Euisung
- Issue Date
- 1-7월-2009
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Algebraic geometry; Projective variety; Minimal free resolution
- Citation
- JOURNAL OF ALGEBRA, v.322, no.1, pp.108 - 121
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF ALGEBRA
- Volume
- 322
- Number
- 1
- Start Page
- 108
- End Page
- 121
- ISSN
- 0021-8693
- Abstract
- For a very ample line bundle L on a projective scheme X, let phi(Ll) : X hooked right arrow PH(0) (X, L(l)), l >= 1, be the embedding defined by the complete linear series |L(l)|. In this paper we study the problem how the Castelnuovo-Mumford regularity of phi(L)(X) effects on the defining equations of phi(Ll)(X) and the syzygies among them. We show that if phi(L)(X) subset of PH(0) (X, L) is m-regular, then (X, L(l)) satisfies property N(2l-m+1) for m/2 <= l <= m - 2, and (X, L(l)) satisfies property N(l) for all l >= m - 1. (C) 2009 Elsevier Inc. All rights reserved.
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