Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Seshadri constants on Jacobian of curves

Author: Jian Kong
Journal: Trans. Amer. Math. Soc. 355 (2003), 3175-3180
MSC (2000): Primary 14H40; Secondary 14K12
Published electronically: April 17, 2003
MathSciNet review: 1974680
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We compute the Seshadri constants on the Jacobian of hyperelliptic curves, as well as of curves with genus three and four. For higher genus curves we conclude that if the Seshadri constants of their Jacobian are less than 2, then the curves must be hyperelliptic.

References [Enhancements On Off] (What's this?)

  • 1. L. Ein and R. Lazarsfeld, Seshadri constants on smooth surfaces, Journées de Géométrie Algébrique d'Orsay (Orsay, 1992), Astérisque 218 (1993), 177-186. MR 95f:14031
  • 2. E. Izadi, The geometric structure of $A_4$, the structure of the Prym map, double solids and $\Gamma_{00}$-divisors, J. Reine Angew. Mathematik 462 (1995), 93-158. MR 96d:14042
  • 3. H. Lange and C. Birkenhake, Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1992. MR 94j:14001
  • 4. R. Lazarsfeld, Lengths of periods and Seshadri constants of abelian varieties, Math. Res. Letters 3 (1996), 439-447. MR 98e:14044
  • 5. M. Nakamaye, Seshadri constants on abelian varieties, Amer. J. Math. 118 (1996), 621-635. MR 97k:14005
  • 6. A. Steffens, Remarks on Seshadri constants, Math. Z. 227 (1998), 505-510. MR 99c:14009
  • 7. G. Welters, The surfaces $C - C$ on Jacobi varieties and second order theta functions, Acta Math. 157 (1986), 1-22. MR 87j:14048

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14H40, 14K12

Retrieve articles in all journals with MSC (2000): 14H40, 14K12

Additional Information

Jian Kong
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218

Keywords: Algebraic geometry, algebraic curves, abelian varieties
Received by editor(s): August 1, 2002
Received by editor(s) in revised form: August 26, 2002
Published electronically: April 17, 2003
Article copyright: © Copyright 2003 American Mathematical Society