Riemann surfaces and generalized theta functions

Robert C. Gunning


  • I. Complex Manifolds and Vector Bundles.- x 1. Complex Manifolds and the Example of the Complex Tori.- x 2. Complex Analytic Vector Bundles and the Example of Line Bundles of Divisors.- x 3. Factors of Automorphy and Complex Analytic Vector Bundles.- II. Riemann Surfaces.- x 4. Markings of Riemann Surfaces and Characteristic Classes of Factors of Automorphy.- x 5. Abelian Differentials and the Jacobi Variety of a Riemann Surface.- x 6. Meromorphic Abelian Differentials and the Prime Function of a Riemann Surface.- III. Generalized Theta Functions.- x 7. Theta Factors of Automorphy and Generalized Theta Functions.- x 8. Generalized Theta Functions and Canonical Subvarieties of the Jacobi Variety.- x 9. Relations Between Theta Factors of Automorphy.- x 10. Dimensions of Spaces of Generalized Theta Functions.- x 11. Induced Theta Factors and Theta Functions on Riemann Surfaces.- IV. Prym Differentials.- x 12. Prym Differentials and Generalized Theta Functions.- x 13. Periods and the Period Matrix for Prym Differentials.- x 14. The Riemann Equality for Prym Periods.- x 15. Regular Prym Differentials.- Appendix. Some Topics in the Classical Theory of Theta Functions.- x 16. Classification of Scalar Factors of Automorphy for Complex Tori.- x 17. Relatively Automorphic Functions: the Theta Series.- x 18. Jacobi Varieties: Abelian and Riemannian Theta Functions.- x 19. Some Analytic Cohomology Groups for Complex Tori.- References.- Index of Theorems.- Index of Notation.

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書名 Riemann surfaces and generalized theta functions
著作者等 Gunning, Robert C.
Gunning R.C.
Gunning R C
シリーズ名 Ergebnisse der Mathematik und ihrer Grenzgebiete
出版元 Springer-Verlag
刊行年月 1976
版表示 Softcover reprint of the original 1st ed. 1976
ページ数 xii, 165 p.
大きさ 25 cm
ISBN 0387077448
NCID BA00759508
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言語 英語
出版国 ドイツ