Silent-Ischemia
发表于 2025-3-26 22:38:53
Bilinear Relations,Before proceeding further, we recall some facts about compact oriented surfaces. We shall not prove them here; proofs can be found in, for example .
Tidious
发表于 2025-3-27 01:58:29
,The Jacobian and Abel’s Theorem,Let . be a compact Riemann surface of genus . ≥ 1. We use the description of . in terms of a convex 4. − gon as in §14, and the corresponding basis .., .. of ..(.).
颂扬本人
发表于 2025-3-27 08:08:04
The Theta Divisor,In this section, we study the influence of the theta divisor on the Riemann surface .. The results were given by Riemann in his fundamental paper on abelian functions. The proofs given here are not very different from Riemann’s.
基因组
发表于 2025-3-27 10:31:03
,Riemann’s Theorem on the Singularities of Θ,Riemann’s singularity theorem expresses the order of vanishing of the ϑ-function at a point ζ . Θ in terms of dim |.|, where . ≥ 0 is a divisor of degree . − 1 with ζ − κ = .. Riemann proves this by relating this order to the vanishing of ϑ on sets of the form .. − .. − ζ (.).
Commodious
发表于 2025-3-27 13:54:15
Some Geometry of Curves in Projective Space,holomorphic line bundle as on a Riemann surface: if {..} is an open covering of . is such that .. ∩ . = {. ∈ ....(.) = 0, .. ≠ 0 at any pomit of ..}, then .. = ../.. is holomorphic, nowhere zero on .. ∩ .. and form the transition functions for a line bundle .. The family {..} define the standard section .. of . (whose divisor is .).
Pastry
发表于 2025-3-27 20:05:36
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煞费苦心
发表于 2025-3-27 22:00:32
https://doi.org/10.1007/978-3-663-11402-4ch pairs (., .) and (., .) are said to be equivalent, and define the same germ of holomorphic function at a, if there exists an open neighbourhood . of ., . ⊂ . ∩ ., such that . = .. An equivalence class is called a germ of holomorphic function at .; the class of a pair (.) is called the germ of . a
EPT
发表于 2025-3-28 04:34:08
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parsimony
发表于 2025-3-28 07:56:21
https://doi.org/10.1007/978-3-531-92469-4holomorphic line bundle as on a Riemann surface: if {..} is an open covering of . is such that .. ∩ . = {. ∈ ....(.) = 0, .. ≠ 0 at any pomit of ..}, then .. = ../.. is holomorphic, nowhere zero on .. ∩ .. and form the transition functions for a line bundle .. The family {..} define the standard sec
游行
发表于 2025-3-28 12:11:20
,Das europäische Mehrebenensystem, torus. Let . be a holomorphic line bundle on ., and π: ℂ. → . the projection. A well-known theorem in complex analysis asserts that any holomorphic line (or even vector) bundle on ℂ. is holomorphically trivial. Let . be a trivialisation. If λ ∈ Λ and . ∈ ℂ., then the isomorphisms . differ by multip