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Transactions of the American Mathematical Society

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On syzygies of abelian varieties

Author: Elena Rubei
Journal: Trans. Amer. Math. Soc. 352 (2000), 2569-2579
MSC (2000): Primary 14K05
Published electronically: March 7, 2000
MathSciNet review: 1624206
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In this paper we prove the following result: Let $X$ be a complex torus and $M$ a normally generated line bundle on $X$; then, for every $p \geq 0$, the line bundle $M^{p+1}$ satisfies Property $ N_{p}$ of Green-Lazarsfeld.

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  • [E-L] L. Ein R. Lazarsfeld, Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension, Invent. Math. 111 (1993) no. 1, 51-67. MR 93m:13006
  • [Gr1] M. Green, Koszul cohomology and the geometry of projective varieties I, II, J. Differential Geom. 19 (1984), 125-171; J. Differential Geom. 20 (1984), 279-289. MR 85e:14022; MR 86j:14011
  • [Gr2] M. Green, Koszul cohomology and geometry, in: (M. Cornalba et al. eds), Lectures on Riemann Surfaces, World Scientific Press (1989). MR 91k:14012
  • [G-L] M. Green and R. Lazarsfeld, On the projective normality of complete linear series on an algebraic curve, Invent. Math. 83 (1986), 73-90. MR 87g:14022
  • [Ha] R. Hartshorne, Algebraic Geometry, Grad. Texts Math. 52, Springer-Verlag, Berlin-Heidelberg-New York, 1977. MR 57:3116
  • [Ke] G. Kempf, Projective cooridinate rings of abelian varieties, in: Algebraic Analysis, Geometry and Number Theory, edited by I.J. Igusa, The John Hopkins Press (1989), 225-236. MR 98m:14047
  • [Ko] S. Koizumi, Theta relations and projective normality of abelian varieties, Amer. J. Math. 98 (1976), 865-889. MR 58:702
  • [L-B] H. Lange and Ch. Birkenhake, Complex Abelian Varieties, Springer-Verlag, 1992. MR 94j:14001
  • [Laz1] R. Lazarsfeld, Projectivité normale des surfaces abéliannes, redigé par O. Debarre. prépublication No. 14 Europroj - C.I.M.P.A., Nice, 1990.
  • [Laz2] R. Lazarsfeld, A sampling of vector bundle techniques in the study of linear series, in: (M. Cornalba et al. (eds), Lectures on Riemann Surfaces, World Scientific Press (1989), 500-559. MR 92f:14006
  • [Mum1] D. Mumford, Varieties defined by quadratic equations in: Questioni sulle varietà algebriche, Corsi C.I.M.E., Edizioni Cremonese, Roma, (1969), 29-100. MR 44:209
  • [Mum2] D. Mumford, On equations defining abelian varieties, Invent. Math. 1 (1966), 287-354. MR 34:4269
  • [Re] I. Reider, Vector bundles of rank $2$ and linear systems on algebraic surfaces, Ann. of Math., 127 (1988), 309-316. MR 89e:14038
  • [Se] T. Sekiguchi, On normal generation by a line bundle on an abelian variety, Proc. Japan Acad. 54, Ser A (1978), 185-188. MR 80c:14026

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Additional Information

Elena Rubei
Affiliation: Dipartimento di Matematica, Università di Pisa, via F. Buonarroti 2, Pisa (PI) c.a.p. 56127, Italia

Keywords: Abelian varieties, syzygies
Received by editor(s): November 30, 1997
Received by editor(s) in revised form: March 29, 1998
Published electronically: March 7, 2000
Additional Notes: This research was carried through in the realm of the AGE Project HCMERBCHRXCT940557 and of the ex-40 MURST Program “Geometria algebrica".
Article copyright: © Copyright 2000 American Mathematical Society