Results 1 to 10 of about 1,594 (81)

A note on the Schottky problem [PDF]

, 2018
In this article, we discuss and survey the recent progress towards the Schottky problem, and make some comments on the relations between the Andr{\'e}-Oort conjecture, Okounkov convex bodies, Coleman's conjecture, stable modular forms, Siegel-Jacobi ...
Yang, Jae-Hyun
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Vector-Valued Modular Forms from the Mumford Form, Schottky-Igusa Form, Product of Thetanullwerte and the Amazing Klein Formula [PDF]

, 2012
Vector-valued Siegel modular forms are the natural generalization of the classical elliptic modular forms as seen by studying the cohomology of the universal abelian variety.
Matone, Marco, Volpato, Roberto
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The non-existence of stable Schottky forms [PDF]

, 2013
Let $A_g^S$ be the Satake compactification of the moduli space $A_g$ of principally polarized abelian $g$-folds and $M_g^S$ the closure of the image of the moduli space $M_g$ of genus $g$ curves in $A_g$ under the Jacobian morphism.
G. Codogni, Igusa, Igusa, Mumford, N. I. Shepherd-Barron, Schottky, Springer   +6 more
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More on superstring chiral measures [PDF]

, 2010
In this paper we study the expressions of the superstring chiral measures for $g\leq 5$. We obtain certain new expressions which are functions of higher powers of theta constants.
Andrianov, Atick, Atick, Belavin, Belavin, Belavin, Cacciatori, Cacciatori, Cacciatori, Cerchiai, D'Hoker, D'Hoker, D'Hoker, Dalla Piazza, Dalla Piazza, Dunin-Barkowski, Frame, Frame, Francesco Dalla Piazza, Grushevsky, Grushevsky, Grushevsky, Igusa, Jacobson, Matone, Matone, Morozov, Morozov, Morozov, Nebe, Oura, Poor, Rauch, Runge, Runge, Sagan, Salvati Manni, Salvati Manni, Salvati Manni, van Geemen, van Geemen, van Geemen   +41 more
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Castelnuovo theory and the geometric Schottky problem

, 2006
We prove and conjecture results which show that Castelnuovo theory in projective space has a close analogue for abelian varieties. This is related to the geometric Schottky problem: our main result is that a principally polarized abelian variety ...
Pareschi, Giuseppe, Popa, Mihnea
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Secants of Abelian Varieties, Theta functions, and Soliton Equations

, 1996
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.
Taimanov, I. A.
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The Schottky problem in genus five [PDF]

, 2012
In this paper, we present a solution to the Schottky problem in the spirit of Schottky and Jung for genus five curves. To do so, we exploit natural incidence structures on the fibers of several maps to reduce all questions to statements about the Prym ...
Siegel, Charles
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Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian

, 2012
A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three.
A Beilinson, A Belavin, A Belavin, A Morozov, A Morozov, AM Polyakov, C Poor, D Mumford, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, E D’Hoker, EP Verlinde, F Dalla Piazza, FD Piazza, FD Piazza, JM Guilarte, M Matone, M Matone, M Matone, M Matone, M Matone, M Matone, M Matone, M Oura, Marco Matone, N Berkovits, P Dunin-Barkowski, R Salvati-Manni, S Grushevsky, S Grushevsky, SL Cacciatori, SL Cacciatori, SL Cacciatori, T Ichikawa, T Ichikawa, Y Manin   +45 more
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Integrable Structure of the Dirichlet Boundary Problem in Multiply-Connected Domains

, 2004
We study the integrable structure of the Dirichlet boundary problem in two dimensions and extend the approach to the case of planar multiply-connected domains.
A Zabrodin, A. Marshakov, Aharonov, I. Krichever, Kazakov, Krichever, Krichever, Marshakov, Mineev-Weinstein, Takasaki, Takhtajan, Wiegmann, Wit   +12 more
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Dispersionless Hirota equations and the genus 3 hyperelliptic divisor [PDF]

, 2019
Equations of dispersionless Hirota type have been thoroughly investigated in the mathematical physics and differential geometry literature. It is known that the parameter space of integrable Hirota type equations in 3D is 21-dimensional and the action of
Cléry, Fabien, Ferapontov, Evgeny V.
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