Titlebook: Riemann Surfaces; Hershel M. Farkas,Irwin Kra Textbook 19801st edition Springer Science+Business Media New York 1980 Abelian variety.Divis

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書目名稱Riemann Surfaces影響因子(影響力)




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要素

Existence Theorems,nt meromorphic functions. We do so by constructing certain harmonic differentials (with singularities). From the existence of harmonic differentials, it is trivial to construct meromorphic differentials. A ratio of two linearly independent meromorphic differentials produces a non-constant meromorphic function.

開始從未

Compact Riemann Surfaces,important theorems concerning compact Riemann surfaces : the RiemannRoch theorem, Abel’s theorem, and the Jacobi inversion theorem. Many applications of these theorems are obtained; and the simplest compact Riemann surfaces, the hyperelliptic ones, are discussed in great detail.

Polydipsia

Theta Functions, the Jacobian variety of a compact surface, and via the embedding of the Riemann surface into its Jacobian variety, multivalued holomorphic functions on the surface. The high point of our present development is the Riemann vanishing theorem (Theorem VI.3.5). Along the way, we will reprove the Jacobi inversion theorem.

LEER

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Riemann Surfaces978-1-4684-9930-8Series ISSN 0072-5285 Series E-ISSN 2197-5612

chandel

Uniformization,This chapter has two purposes. The first and by far the most important is to prove the uniformization theorem for Riemann surfaces. This theorem describes all simply connected Riemann surfaces and hence with the help of topology, all Riemann surfaces.

GLIB

,Automorphisms of Compact Surfaces — Elementary Theory,In this chapter we develop the basic results on the automorphism group of a compact Riemann surface, continuing the study began in III.7. Some of the deeper results will have to await the creation of more powerful machinery.

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不適當

https://doi.org/10.1007/978-1-4684-9930-8Abelian variety; Divisor; Hilbert space; Jacobi; Riemann surface; Riemannsche Fl?che; Surfaces; Volume; addi