Notes on the inversion of integrals. II

Author:
George R. Kempf

Journal:
Proc. Amer. Math. Soc. **108** (1990), 59-67

MSC:
Primary 14H40; Secondary 14K05, 14K25

MathSciNet review:
990426

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Abstract: If is a Picard bundle on the Jacobian of a curve , we have the problem of describing globally. The theta divisor is ample on . Thus it is possible to write as the sheaf associated to a graded over the well-known ring . In this paper we compute the degree of generators and relations for such a module .

**[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]**-,*Deformations of symmetric products*, in "Riemann Surfaces and Related Topics", Proceeding of the 1978 Stony Brook Conference, Princeton University Press, Princeton, 1980.**[3]**-,*Multiplication over abelian varieties*, (to appear).**[4]**George R. Kempf,*Notes of the inversion of integrals. I*, Proc. Amer. Math. Soc.**107**(1989), no. 4, 873–880. MR**986651**, 10.1090/S0002-9939-1989-0986651-X**[5]**Shoji Koizumi,*Theta relations and projective normality of Abelian varieties*, Amer. J. Math.**98**(1976), no. 4, 865–889. MR**0480543****[6]**Shoji Koizumi,*The rank theorem on matrices of theta functions*, J. Fac. Sci. Univ. Tokyo Sect. IA Math.**24**(1977), no. 1, 115–122. MR**0480544****[7]**D. Mumford,*On the equations defining abelian varieties. I*, Invent. Math.**1**(1966), 287–354. MR**0204427****[8]**-,*Varieties defined by quadratic equations*, in "Questions on Algebraic Varieties", Centro Inter. Mate. Estrivo, Roma, 1970, 31-100.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-0990426-3

Keywords:
Algebraic curves,
Jacobians and Picard bundles

Article copyright:
© Copyright 1990
American Mathematical Society