Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Notes of the inversion of integrals. I

Author: George R. Kempf
Journal: Proc. Amer. Math. Soc. 107 (1989), 873-880
MSC: Primary 14H40; Secondary 14K05, 14K25
MathSciNet review: 986651
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ W$ is a Picard bundle on the Jacobian $ J$ of a curve $ C$, we have the problem of describing $ W$ globally. The theta divisor $ \theta $ is ample on $ J$. Thus it is possible to write $ {n^ * }W$ as the sheaf associated to a graded $ M$ over the well-known ring $ { \oplus _{m \geq 0}}\Gamma (J,{\mathcal{O}_J}(m4\theta ))$. In this paper we compute the degree of generators and relations for such a module $ M$.

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

  • [1] G. Kempf, Toward the inversion of abelian integrals II, Amer. J. Math. 101 (1979), 184-202. MR 527831 (82a:14010b)
  • [2] -,Some metrics on Picard bundles, in "Vector Bundles on Algebraic Varieties," Tata Institute, Bombay, pp. 217-224. MR 893600 (88j:14039)
  • [3] D. Mumford, On the equations defining abelian varieties I, II, III, Inventiones Math. 1 (1966) 287-354; 3 (1967) 75-135 and 215-244. MR 0204427 (34:4269)
  • [4] -, Varieties defined by quadratic equations, in "Questions on Algebraic Varieties," Centro Inter. Mate, Estrivo, Roma (1970), 31-100.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14H40, 14K05, 14K25

Retrieve articles in all journals with MSC: 14H40, 14K05, 14K25

Additional Information

Keywords: Algebraic curves, Jacobians, Picard bundles
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society