scholarly journals Finiteness property for generalized abelian integrals

2003 ◽  
Vol 53 (3) ◽  
pp. 767-785 ◽  
Author(s):  
Rémi Soufflet
Keyword(s):  
Abelian Integrals ◽  
Finiteness Property

On multiple curves. II

1945 ◽  
Vol 41 (2) ◽  
pp. 117-126
Author(s):  
W. V. D. Hodge
Keyword(s):  
Algebraic Curve ◽  
Abelian Integrals

In this note I consider the Abelian integrals of the first kind on an algebraic curve Γ which is a normal multiple of a curve C, as defined in Note I*.

Aspherical manifolds, Mellin transformation and a question of Bobadilla–Kollár

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yongqiang Liu ◽  
Laurenţiu Maxim ◽  
Botong Wang
Keyword(s):  
Integral Homology ◽  
Algebraic Varieties ◽  
Finiteness Property ◽  
Rational Homology ◽  
Mellin Transformation ◽  
Hopf Conjecture ◽  
Ball Quotients ◽  
Proper Map ◽  
Complex Projective ◽  
Aspherical Manifolds

Abstract In their paper from 2012, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this paper, we answer positively the integral homology version of their question in the case of abelian varieties, and the rational homology version in the case of compact ball quotients. We also propose several conjectures in relation to the Singer–Hopf conjecture in the complex projective setting.

scholarly journals Moments on Riemann surfaces and hyperelliptic Abelian integrals

2014 ◽  
Vol 89 (1) ◽  
pp. 125-155
Author(s):  
Lubomir Gavrilov ◽  
Fedor Pakovich
Keyword(s):  
Riemann Surfaces ◽  
Abelian Integrals

Finitude simple et structures o-minimales (Finiteness property implies o-minimality)

2002 ◽  
Vol 67 (4) ◽  
pp. 1616-1622 ◽  
Author(s):  
Jean-Marie Lion
Keyword(s):  
A Priori ◽  
Finiteness Property

RésuméL'objet de ce texte est de montrer que des fonctions qui appartiennent à une famille vérifiant une propriété de finitude a priori non uniforme sont en fait définissables dans une structure o-minimale.

scholarly journals Theta Surfaces

2020 ◽  
Author(s):  
Daniele Agostini ◽  
Türkü Özlüm Çelik ◽  
Julia Struwe ◽  
Bernd Sturmfels
Keyword(s):  
Algebraic Geometry ◽  
Theta Functions ◽  
Minkowski Sum ◽  
Zero Set ◽  
Analytic Surface ◽  
Numerical Algebraic Geometry ◽  
Abelian Integrals ◽  
Space Curves ◽  
Quartic Curves ◽  
Special Plane

Abstract A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincaré showed that any analytic surface that is the Minkowski sum of two space curves in two different ways is a theta surface. The four space curves that generate such a double translation structure are parametrized by abelian integrals, so they are usually not algebraic. This paper offers a new view on this classical topic through the lens of computation. We present practical tools for passing between quartic curves and their theta surfaces, and we develop the numerical algebraic geometry of degenerations of theta functions.

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