沟通
发表于 2025-3-25 07:13:46
Complex Tori,The lattice . in a real or complex finite dimensional vector space . is a discrete subgroup such that the quotient group . is compact. The lattice . is a free Abelian group of rank equal to the real dimension of . and the induced mapping . ⊗. ℝ → . is an isomorphism and conversely.
吝啬性
发表于 2025-3-25 09:29:13
The Existence of Sections of Sheaves,Let (.) be A.-H. data for a complex torus .. Our objective is
最小
发表于 2025-3-25 13:19:03
The Cohomology of Complex Tori,Let . be a lattice in a real vector space .. Then the quotient . is a real torus. Using a basis .,..., . of . we have an isomorphism . which sends a real .-vector (λ.,..., λ.) to the .-coset ∑λ.. Thus a real torus is topologically isomorphic to a product of circles. Consequently the algebraic topology of . is obvious.
Eviction
发表于 2025-3-25 19:29:45
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ERUPT
发表于 2025-3-25 21:19:22
Theta Functions,Let . be a free abelian group of finite rank with a non-degenerate integral-valued skew-symmetric form . → ℤ. In this section we will develop the structure of the symplectic lattice ..
A保存的
发表于 2025-3-26 02:03:47
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枫树
发表于 2025-3-26 05:10:34
Moduli Spaces,Let . be a real vector space of dimension 2. with a non-degenerate skew-symmetric form .. Recall the symplectic group Sym.(.) consists of all ℝ-linear transformations . of . such that . for all . and . in ..
mucous-membrane
发表于 2025-3-26 12:17:34
Mappings to Abelian Varieties,Let . be a complex torus and let . be a smooth connected variety. Let . be a fixed point of .. Let . be an analytic mapping. Then we have the pull-back mapping of differentials . : . = .) → .).
isotope
发表于 2025-3-26 14:03:28
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Isometric
发表于 2025-3-26 20:01:27
Abelian Varieties Occurring in Nature,Let . be a free abelian group of rank 2.. An elementary structure on . is a complex subspace . of .⊗. ℂ such that .⊗. ℂ = . where . is the linear mapping induced by complex conjugation in ℂ. Thus dim. . = dim. .. Let π. and π. denote projective of . ⊗. ℂ onto . and ..