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Proceedings of the American Mathematical Society

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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
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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] George Kempf, Toward the inversion of abelian integrals. II, Amer. J. Math. 101 (1979), no. 1, 184–202. MR 527831, 10.2307/2373944
  • [2] G. R. Kempf, Some metrics on Picard bundles, Vector bundles on algebraic varieties (Bombay, 1984) Tata Inst. Fund. Res. Stud. Math., vol. 11, Tata Inst. Fund. Res., Bombay, 1987, pp. 217–224. MR 893600, 10.1002/neu.480180207
  • [3] D. Mumford, On the equations defining abelian varieties. I, Invent. Math. 1 (1966), 287–354. MR 0204427
  • [4] -, Varieties defined by quadratic equations, in "Questions on Algebraic Varieties," Centro Inter. Mate, Estrivo, Roma (1970), 31-100.

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