Gallego Rodrigo, Francisco Javier and Purnaprajna, Bangere P.
(2001)
*Some results on rational surfaces and Fano varieties.*
Journal fur die Reine und Angewandte Mathematik, 538
.
pp. 25-55.
ISSN 0075-4102

PDF
Restringido a Repository staff only hasta 2020. 313kB |

Official URL: http://arxiv.org/pdf/math/0001107v1.pdf

## Abstract

The goal of this article is to study the equations and syzygies of embeddings of rational surfaces and certain Fano varieties. Given a rational surface X and an ample and base-point-free line bundle L on X, we give an optimal numerical criterion for L to satisfy property N-p. This criterion turns out to be a characterization of property N-p if X is anticanonical. We also prove syzygy results for adjunction bundles and a Reider type theorem for higher syzygies

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Rational surface; Fano variety; line bundle; Syzygy;property Np; Adjunction bundles; Koszul cohomology |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 15391 |

References: | M.C. Beltrametti and A.J. Sommese, The Adjunction Theory of Complex Projective Varieties,Walter de Gruyter, 1995. D. Butler, Normal generation of vector bundles over a curve, J. Differential Geometry 39 (1994) 1-34. L. Ein and R. Lazarsfeld, Koszul cohomology and syzygies of projective varieties, Inv. Math.111 (1993), 51-67. F.J. Gallego and B.P. Purnaprajna Normal presentation on elliptic ruled surfaces, J. Algebra 186, (1996), 597-625. Higher syzygies of elliptic ruled surfaces, J. Algebra 186, (1996), 626-659. Very ampleness and higher syzygies for Calabi-Yau threefolds, Math. Ann. 312 (1998),133-149. Projective normality and syzygies of algebraic surfaces, J. reine angew. Math. 506 (1999), 145-180. Vanishing theorems and syzygies for K3 surfaces and Fano varieties, to appear in J. Pure App. Alg. M. Green, Koszul cohomology and the geometry of projective varieties, J. Differential Geometry 19 (1984), 125-171. M. Green and R. Lazarsfeld, Some results on the syzygies of finite sets and algebraic curves, Compositio Math. 67 (1989), 301-314. B. Harbourne, Anticanonical rational surfaces, Trans. A. M. S. 349 (1997), 1191-1208. Birational morphisms of rational surfaces, J. Algebra 190 (1997), 145-162. R. Hartshorne, Algebraic Geometry, Springer–Verlag 1977. Y. Homma, Projective normality and the defining equations of ample invertible sheaves on elliptic ruled surfaces with e ≥ 0, Natural Science Report, Ochanomizu Univ. 31 (1980)61-73. Projective normality and the defining equations of an elliptic ruled surface with negative invariant, Natural Science Report, Ochanomizu Univ. 33 (1982) 17-26. T. Josefiak, P. Pragacz and J. Weyman, Resolutions of determinantal varieties and tensor complexes associated with symmetric and antisymmetric matrix, Asterisque 87-88 (1981),109-189. Y. Miyaoka, The Chern class and Kodaira dimension of a minimal variety, Algebraic Geometry –Sendai 1985, Advanced Studies in Pure Math., Vol. 10, North-Holland, Amsterdam, 449-476. D. Mumford Varieties defined by quadratic equations, Corso CIME in Questions on Algebraic Varieties, Rome, 1970,30-100. G. Ottaviani and R. Paoletti, Syzygies of Veronese embeddings, preprint. |

Deposited On: | 28 May 2012 09:32 |

Last Modified: | 06 Feb 2014 10:23 |

Repository Staff Only: item control page