Author | Gunning, Robert C. author |
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Title | Riemann Surfaces and Generalized Theta Functions [electronic resource] / by Robert C. Gunning |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1976 |
Connect to | http://dx.doi.org/10.1007/978-3-642-66382-6 |
Descript | XII, 168 p. online resource |
I. Complex Manifolds and Vector Bundles -- ยง 1. Complex Manifolds and the Example of the Complex Tori -- ยง 2. Complex Analytic Vector Bundles and the Example of Line Bundles of Divisors -- ยง 3. Factors of Automorphy and Complex Analytic Vector Bundles -- II. Riemann Surfaces -- ยง 4. Markings of Riemann Surfaces and Characteristic Classes of Factors of Automorphy -- ยง 5. Abelian Differentials and the Jacobi Variety of a Riemann Surface -- ยง 6. Meromorphic Abelian Differentials and the Prime Function of a Riemann Surface -- III. Generalized Theta Functions -- ยง 7. Theta Factors of Automorphy and Generalized Theta Functions -- ยง 8. Generalized Theta Functions and Canonical Subvarieties of the Jacobi Variety -- ยง 9. Relations Between Theta Factors of Automorphy -- ยง 10. Dimensions of Spaces of Generalized Theta Functions -- ยง 11. Induced Theta Factors and Theta Functions on Riemann Surfaces -- IV. Prym Differentials -- ยง 12. Prym Differentials and Generalized Theta Functions -- ยง 13. Periods and the Period Matrix for Prym Differentials -- ยง 14. The Riemann Equality for Prym Periods -- ยง 15. Regular Prym Differentials -- Appendix. Some Topics in the Classical Theory of Theta Functions -- ยง 16. Classification of Scalar Factors of Automorphy for Complex Tori -- ยง 17. Relatively Automorphic Functions: the Theta Series -- ยง 18. Jacobi Varieties: Abelian and Riemannian Theta Functions -- ยง 19. Some Analytic Cohomology Groups for Complex Tori -- References -- Index of Theorems -- Index of Notation