Results 1 to 10 of about 161 (99)

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
Sergei Starchenko, Ya'Acov Peterzil
exaly   +5 more sources

Theta Functions and Adiabatic Curvature on an Abelian Variety

Journal of Geometric Analysis
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
Jih-Hsin Cheng, Cheng Jih-Hsin
exaly   +4 more sources

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.
openaire   +2 more sources

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 ...
openaire   +3 more sources

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 ...
openaire   +2 more sources

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.
openaire   +3 more sources

Abelian varieties and theta functions associated to compact Riemannian manifolds; constructions inspired by superstring theory

Journal de Mathématiques Pures et Appliquées, 2012
A few corrections, final ...
Müller-Stach, S., Peters, C., Srinivas, V.   +2 more
openaire   +3 more sources

On Nonlinear Equations Integrable in Theta Functions of Nonprincipally Polarized Abelian Varieties

Siberian Mathematical Journal, 2001
LaTeX, 14 ...
openaire   +2 more sources

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 ( T
openaire   +2 more sources

From Quantum Curves to Topological String Partition Functions. [PDF]

Commun Math Phys, 2023
Coman I, Pomoni E, Teschner J.
europepmc   +1 more source