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Vanishing theorems and syzygies for K3 surfaces and Fano varieties.

Gallego Rodrigo, Francisco Javier and Purnaprajna, Bangere P. (2000) Vanishing theorems and syzygies for K3 surfaces and Fano varieties. Journal of Pure and Applied Algebra , 146 (3). pp. 251-265. ISSN 0022-4049

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Abstract

In this article we prove results concerning the vanishing of Koszul cohomology groups on K3 surfaces and n-dimensional Fano varieties of index n - 2. As an application of these vanishings we obtain results on projective normality and syzygies for K3 surfaces and Fano varieties.

Item Type:Article
Uncontrolled Keywords:Vanishing theorems; Syzygies; K3 surface; Fano n-folds; Line bundle
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15413
References:

D. Butler, Normal generation of vector bundles over a curve, J. Dierential Geometry 39 (1994) 1{34.

L. Ein, R. Lazarsfeld, Koszul cohomology and syzygies of projective varieties, Inv. Math. 111 (1993)51{ 67.

F. Gallego, B.P. Purnaprajna, Projective normality and syzygies of algebraic surfaces, J. Reine Angew.Math.,to appear.

M. Green, Koszul cohomology and the geometry of projective varieties, J. Dierential Geometry 19 (1984) 125{171.

V.A. Iskovskih, Fano 3-folds I, Math. USSR Izvestija 11(1977) 485{528.

V.A. Iskovskih, Fano 3-folds II, Math. USSR Izvestija 12 (1978) 469{506.

A. Mayer, Families of K-3 surfaces, Nagoya Math. J. 48 (1972) 1{17.

Y. Miyaoka, The Chern class and Kodaira dimension of a minimal variety, in: Algebraic Geometry, Sendai, 1985, Adv. Studies in Pure Math., vol 10, pp. 449{476.

K. Paranjape, S. Ramanan, On the canonical ring of a curve, in: Algebraic Geometry and Commutative Algebra in Honor of Nagata, vol 2, pp. 503{516.

G. Pareschi, B.P. Purnaprajna, Canonical ring of a curve is Koszul: a simple proof, Illinois J. Math. 41 (1997) 266-271.

B. Saint-Donat, On projective models of K3 surfaces, Amer. J. Math. 96 (1974) 602{ 639.

C.S. Seshadri, Vector bundles on curves, in: Linear Algebraic Groups and Their Representations, Los Angeles, 1992, Contemporary Math., vol. 153, American Mathematical Society, Providence, RI, 1993,pp. 163{200.

Deposited On:30 May 2012 08:46
Last Modified:06 Feb 2014 10:24

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