Biblioteca de la Universidad Complutense de Madrid

Projective normality and syzygies of algebraic surfaces


Gallego Rodrigo, Francisco Javier y Purnaprajna, Bangere P. (1999) Projective normality and syzygies of algebraic surfaces. Journal für die reine und angewandte Mathematik, 506 . pp. 145-180. ISSN 0075-4102

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 2020.

Vista previa

URL Oficial:


In this work we develop new techniques to compute Koszul cohomology groups for several classes of varieties. As applications we prove results on projective normality and syzygies for algebraic surfaces. From more general results we, obtain in particular the following: (a) Mukai's conjecture (and stronger variants of it) regarding projective normality and normal presentation for surfaces with Kodaira dimension 0, and uniform bounds for higher syzygies associated to adjoint linear series, (b) effective bounds along the lines of Mukai's conjecture regarding projective normality and normal presentation for surfaces of positive Kodaira dimension, and, (c) results on projective normality for pluricanonical models of surfaces of general type (recovering and strengthening results by Ciliberto) and generalizations of them to higher syzygies. In addition, we also extend the above results to singular surfaces.

Tipo de documento:Artículo
Información Adicional:

Erratum ibid. 523, 233-234 (2000)

Palabras clave:Koszul cohomology; Projective normality; Syzygies; Enriques surfaces; Adjoint bundles; surfaces of general type
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:15414

E. Bombieri, Canonical models of surfaces of general type, Inst. Hautes Ét. Sci. Publ. Math. 42 (1973),171—219.

D. Butler, Normal generation of vector bundles over a curve, J. Diff . Geom. 39 (1994)1, —34 .

F. Catanese, Canonical rings and special surfaces of general type, Proceedings of the Summer Research

Institute on Algebraic Geometry at Bowdoin 1985, Part 1, AMS (1987), 175—194.

C. Ciliberto, Sul grado dei generatori dell’anello canonico di una superficie di tipo generate, Rend. Sem. Mat. Univ. Politecn. Torino 41 (1983), 83—111.

F. R. Cossec and I. V. Dolgachev, Enriques Surfaces I, Birkhäuser, 1989.

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

D. Eisenbud, J. Koh, M. Stillman, Determinantal equations for curves of high degree , Amer . J . Math .11 0(1988 )5,13 —539 .

G. Fernandez del Busto, A Matsusaka-type theorem on surfaces , J . Alg . Geom . 5 (1996) , 513—520 .

M. Finkelberg and A . Vishik , The coordinate ring o f a genera l curv e o f genus $ i s Koszul , J . Algebra 16 2 (1993) , 535—539 .

F.J. Gallego and B.P . Purnaprajna , Normal presentation on ellipti c ruled surfaces , J . Algebra 18 6 (1996) ,597—625.

F.J. Gallego and B.P . Purnaprajna , Highe r syzygie s o f elliptic ruled surfaces , J . Algebr a 18 6 (1996) ,626—659.

F.J. Gallego and B.P . Purnaprajna , Vanishing theorems and syzygie s fo r K3 surface s and Fano varieties ,J . Pure App. Alg. , to appear .

F.J. Gallego and B.P . Purnaprajna , Ver y amplenes s and highe r syzygie s fo r Calabi-Yau threefolds , Math .Ann . 31 2 (1998) , 133—149 .

M. Green, Koszul cohomology and the geometry of projective varieties , J . Dif f . Geom . 1 9 (1984) , 125—171 .

M. Green, Koszul cohomology and the geometry o f projective varietie s II, J . Diff . Geom . 2 0 (1984) ,279—289.

M. Green, Koszul cohomology and geometry , Lectures on Riemann Surfaces , Worl d Scientifi c Press ,Singapore (1989) , 177—200 .

Y. Homma, Projectiv e normality and the definin g equations o f ample invertible sheaves on elliptic ruled surface s with $, Natural Scienc e Report, Ochanomizu Univ . 3 1(1980) , 61—73 .

Y. Homma, Projectiv e normality and the defining equations o f an ellipti c ruled surfac e with negative

invariant , Natural Scienc e Report, Ochanomizu Univ . 33 (1982) ,17—26 .

T. Kawachi an d V. Maşek , Reider-type theorems on norma l surfaces , preprint .

Y. Kawamata, The cone o f curve s o f algebraic varieties , Ann . Math. (2 ) 11 9 (1984) , 603—633 .

G. Kemp f , Projectiv e coordinate ring s o f Abelian varieties , Algebraic Analysis , Geometry and Number Theory, the John Hopkins Univ. Press (1989), 225—235.

R. Lazarsfeld, A sampling of vector bundle techniques in the study of linear series, Lectures on Riemann Surfaces, World Scientific Press, Singapore (1989), 500—559.

Y. Miyaoka, The Chern class and Kodaira dimension of a minimal variety, Algebraic Geometry—Sendai 1985, Adv. Stud. Pure Math. 10, North-Holland, Amsterdam (1985), 449—476.

D. Mumford, Varieties defined by quadratic equations, Corso CIME in Questions on Algebraic Varieties,Rome (1970),30—100.

G. Pareschi, Koszul algebras associated to adjunction bundles, J. Algebra 157 (1993), 161—169.

G. Pareschi, Gaussian maps and multiplication maps on certain projective varieties, Comp. Math. 98(1995), 219—268.

G. Pareschi and B. P. Purnaprajna, Canonical ring of a curve is Koszul: A simple proof, Ill. J. Math., to appear.

I. Reider, Vector bundles of rank 2 and linear systems on an algebraic surface, Ann. Math. (2) 127 (1988),309—316.

F. Sakai, Reider-Serrano’s method on normal surfaces, Algebraic Geometry: Proceedings, L’Aquila 1988,Lect. Notes 1417 (1990), 301—319.

V. V. Shokurov, A nonvanishing theorem, Math. USSR-Izv. 26 (1985), 591—604.

Depositado:29 May 2012 09:19
Última Modificación:07 Abr 2015 08:06

Sólo personal del repositorio: página de control del artículo