Secants of Abelian varieties, theta functions, and soliton equations [PDF]
Russian Mathematical Surveys, 1997 This paper is a survey on relations between secant identities and soliton equations and applications of soliton equations to problems of algebraic geometry, i.e., the Riemann-Schottky problem and its analogues. A short introduction into the analytic theory of theta functions is also given.
I. A. Taĭmanov
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Definability of restricted theta functions and families of abelian varieties [PDF]
Duke Mathematical Journal, 2013 We consider some classical maps from the theory of abelian varieties and their moduli spaces and prove their definability, on restricted domains, in the o-minimal structure $\Rae$. In particular, we prove that the embedding of moduli space of principally polarized ableian varierty, $Sp(2g,\Z)\backslash \CH_g$, is definable in $\Rae$, when restricted to
Peterzil, Ya’acov, Starchenko, Sergei
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Theta Functions and Adiabatic Curvature on an Abelian Variety [PDF]
The Journal of Geometric Analysis, 2022 For an ample line bundle $L$ on an Abelian variety $M$, we study the theta functions associated with the family of line bundles $L\otimes T$ on $M$ indexed by $T\in \text{Pic}^{0}(M)$. Combined with an appropriate differential geometric setting, this leads to an explicit curvature computation of the direct image bundle $E$ on $\text{Pic}^{0}(M)$, whose
Ching-Hao Chang +2 more
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Abelian varieties and theta functions associated to compact Riemannian manifolds; constructions inspired by superstring theory [PDF]
Journal de Mathématiques Pures et Appliquées, 2012 A few corrections, final ...
Müller-Stach, S. +2 more
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Ultrametric theta functions and abelian varieties [PDF]
Nagoya Mathematical Journal, 1978 Let k be a field complete with respect to a non-trivial, non-archimedean valuation and let g be a positive integer. Consider the following question : if Γ is a multiplicative subgroup of Gg = (k*)g satisfying certain “Riemann conditions”, can one construct in a natural way an abelian variety defined over k having Gg/Γ as its set of k-rational points ...
Horacio Tapia-Recillas
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On Theta Functions and Abelian Varieties over Valuation Fields of Rank One: (II) Theta Functions and Abelian Functions of Characteristicp(>0) [PDF]
Nagoya Mathematical Journal, 1962 It may safely said that one of the most important problems in modern algebraic geometry is to elevate theory of abelian functions to the same level as theory of elliptic functions beyond the modern formulation of classical results. Being concerned in such a problem, we feel that one of the serious points is the lack of knowladge on the explicit ...
Hisasi Morikawa
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Theta Functions and Abelian Varieties over Valuation Fields of Rank one I [PDF]
Nagoya Mathematical Journal, 1962 We shall denote by the Z-module of integral vectors of dimension r, by T a symmetric complex matrix with positive definite imaginary part and by g the variable vector. If we put and the fundamental theta function is expressed in the form: as a series in q and u.
Hisasi Morikawa
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Mirror symmetry of abelian varieties and multi-theta functions
Journal of Algebraic Geometry, 2002 We study homological mirror symmetry conjecture of symplectic and complex torus. We will associate a mirror torus(T2n,ω+−1B)∧(T^{2n},\omega +\sqrt {-1}B)^{\wedge }to each symplectic torus(T2n,ω)(T^{2n},\omega )together with a closed 2 formBBwhich we call aBB-field. We will associate a coherent sheafE(L,L){\mathcal E}(L,{\mathcal L})on(T2n,ω+−1B)∧(T^{2n}
Kenji Fukaya
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Book Review: Abelian varieties, theta functions and the Fourier transform [PDF]
Bulletin of the American Mathematical Society, 2005 Arnaud Beauville
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Abelian Varieties, Theta Functions and the Fourier Transform [PDF]
, 2003 Alexander Polishchuk
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