TY - JOUR
T1 - On syzygies of Veronese embedding of arbitrary projective varieties
AU - Park, Euisung
N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009/7/1
Y1 - 2009/7/1
N2 - For a very ample line bundle L on a projective scheme X, let φLℓ : X {right arrow, hooked} P H0 (X, Lℓ), ℓ ≥ 1, be the embedding defined by the complete linear series | Lℓ |. In this paper we study the problem how the Castelnuovo-Mumford regularity of φL (X) effects on the defining equations of φLℓ (X) and the syzygies among them. We show that if φL (X) ⊂ P H0 (X, L) is m-regular, then (X, Lℓ) satisfies property N2 ℓ - m + 1 for frac(m, 2) ≤ ℓ ≤ m - 2, and (X, Lℓ) satisfies property Nℓ for all ℓ ≥ m - 1.
AB - For a very ample line bundle L on a projective scheme X, let φLℓ : X {right arrow, hooked} P H0 (X, Lℓ), ℓ ≥ 1, be the embedding defined by the complete linear series | Lℓ |. In this paper we study the problem how the Castelnuovo-Mumford regularity of φL (X) effects on the defining equations of φLℓ (X) and the syzygies among them. We show that if φL (X) ⊂ P H0 (X, L) is m-regular, then (X, Lℓ) satisfies property N2 ℓ - m + 1 for frac(m, 2) ≤ ℓ ≤ m - 2, and (X, Lℓ) satisfies property Nℓ for all ℓ ≥ m - 1.
KW - Algebraic geometry
KW - Minimal free resolution
KW - Projective variety
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U2 - 10.1016/j.jalgebra.2009.03.022
DO - 10.1016/j.jalgebra.2009.03.022
M3 - Article
AN - SCOPUS:67349271259
VL - 322
SP - 108
EP - 121
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
IS - 1
ER -