Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On syzygies of abelian varieties
HTML articles powered by AMS MathViewer

by Elena Rubei PDF
Trans. Amer. Math. Soc. 352 (2000), 2569-2579 Request permission

Abstract:

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.
References
  • Lawrence Ein and Robert Lazarsfeld, Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension, Invent. Math. 111 (1993), no. 1, 51–67. MR 1193597, DOI 10.1007/BF01231279
  • Mark L. Green, Koszul cohomology and the geometry of projective varieties, J. Differential Geom. 19 (1984), no. 1, 125–171. MR 739785
  • Mark L. Green, Koszul cohomology and geometry, Lectures on Riemann surfaces (Trieste, 1987) World Sci. Publ., Teaneck, NJ, 1989, pp. 177–200. MR 1082354
  • Mark Green and Robert Lazarsfeld, On the projective normality of complete linear series on an algebraic curve, Invent. Math. 83 (1986), no. 1, 73–90. MR 813583, DOI 10.1007/BF01388754
  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
  • George R. Kempf, Projective coordinate rings of abelian varieties, Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988) Johns Hopkins Univ. Press, Baltimore, MD, 1989, pp. 225–235. MR 1463704
  • Shoji Koizumi, Theta relations and projective normality of Abelian varieties, Amer. J. Math. 98 (1976), no. 4, 865–889. MR 480543, DOI 10.2307/2374034
  • Herbert Lange and Christina Birkenhake, Complex abelian varieties, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 302, Springer-Verlag, Berlin, 1992. MR 1217487, DOI 10.1007/978-3-662-02788-2
  • R. Lazarsfeld, Projectivité normale des surfaces abéliannes, redigé par O. Debarre. prépublication No. 14 Europroj - C.I.M.P.A., Nice, 1990.
  • Robert Lazarsfeld, A sampling of vector bundle techniques in the study of linear series, Lectures on Riemann surfaces (Trieste, 1987) World Sci. Publ., Teaneck, NJ, 1989, pp. 500–559. MR 1082360
  • David Mumford, Varieties defined by quadratic equations, Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969) Edizioni Cremonese, Rome, 1970, pp. 29–100. MR 0282975
  • D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287–354. MR 204427, DOI 10.1007/BF01389737
  • Igor Reider, Vector bundles of rank $2$ and linear systems on algebraic surfaces, Ann. of Math. (2) 127 (1988), no. 2, 309–316. MR 932299, DOI 10.2307/2007055
  • Tsutomu Sekiguchi, On the normal generation by a line bundle on an Abelian variety, Proc. Japan Acad. Ser. A Math. Sci. 54 (1978), no. 7, 185–188. MR 510946
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14K05
  • Retrieve articles in all journals with MSC (2000): 14K05
Additional Information
  • Elena Rubei
  • Affiliation: Dipartimento di Matematica, Università di Pisa, via F. Buonarroti 2, Pisa (PI) c.a.p. 56127, Italia
  • Email: rubei@mail.dm.unipi.it
  • 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".
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2569-2579
  • MSC (2000): Primary 14K05
  • DOI: https://doi.org/10.1090/S0002-9947-00-02398-9
  • MathSciNet review: 1624206