Higher syzygies of ruled varieties over a curve
نویسندگان
چکیده
منابع مشابه
On Higher Syzygies of Ruled Varieties over a Curve
For a vector bundle E of rank n + 1 over a smooth projective curve C of genus g, let X = PC(E) with projection map π : X → C. In this paper we investigate the minimal free resolution of homogeneous coordinate rings of X . We first clarify the relations between higher syzygies of very ample line bundles on X and higher syzygies of Veronese embedding of fibres of π by the same line bundle. More p...
متن کاملOn Syzygies of Ruled Varieties over a Curve
In this article we concern higher syzygies of line bundles on X = PC(E) where E is a vector bundle of rank n+1 over a smooth projective curve C of genus g. Let H be the tautological line bundle of X and projection π : X → C. Our main result is that for a = 1 or n = 1 or n = 2 and a = 2 (i.e. scrolls of arbitrary dimension or ruled surfaces or quadric surface fibrations), aH+π∗B satisfies Proper...
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The purpose of this article is to study the minimal free resolution of homogeneous coordinate rings of elliptic ruled surfaces. Let X be an irreducible projective variety and L a very ample line bundle on X , whose complete linear series defines the morphism φL : X −→ P(H (L)) Let S = ⊕∞ m=0 S H(X,L) and R(L) ⊕∞ m=0 H (X,L). Since R(L) is a finitely generated graded module over S, it has a mini...
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We study higher syzygies of a ruled surface X over a curve of genus g with the numerical invariant e. Let L ∈ PicX be a line bundle in the numerical class of aC0 + bf . We prove that for 0 ≤ e ≤ g − 2, L satisfies Property Np if a ≥ p + 2 and b − ae ≥ 3g − e + p and for e ≥ g − 1, L satisfies Property Np if a ≥ p + 2 and b − ae ≥ 2g + 1 + p. By using these facts, we obtain Mukai type results. F...
متن کاملOn Higher Syzygies of Ruled Surfaces Ii
In this article we we continue the study of property Np of irrational ruled surfaces begun in [12]. Let X be a ruled surface over a curve of genus g ≥ 1 with a minimal section C0 and the numerical invariant e. When X is an elliptic ruled surface with e = −1, there is an elliptic curve E ⊂ X such that E ≡ 2C0 − f . And we prove that if L ∈ PicX is in the numerical class of aC0 + bf and satisfies...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.08.015