An explicit formula for period determinant
type: Item
instance of: scholarly article
title: An explicit formula for period determinant
zbMATH Open document ID: 1140.32011
author: Alexey A. Glutsyuk
publication date: 2007-04-24T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10175
review text: In this paper the author calculates the determinant of the period matrix associated to a generic complex polynomial in two variables \(H(x,y)\), a basis in the first cohomology group of a nonsingular level curve of \(H\) and a set of complex homogeneous polynomial 1-forms. An explicit formula for the period determinant has been computed before by A. N. Varchenko, but only up to a constant factor depending on the degree of the polynomial. In the present paper the author computes the constant factor. The computations are made gradually, first for a special form set and then for the general case.
reviewed by: Corina Baciu
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 32S10
Mathematics Subject Classification ID: 32S30
Mathematics Subject Classification ID: 14K20
Mathematics Subject Classification ID: 32S20
zbMATH DE Number: 5145714
zbMATH Keywords: period matrices
zbMATH Keywords: monodromy
zbMATH Keywords: vanishing cycles
zbMATH Keywords: Abelian integrals
MaRDI profile type: Publication
OpenAlex ID: W2482143138
cites work: Q3334648
cites work: Equations différentielles à points singuliers réguliers
cites work: Algebraic Gauss-Mann systems and Brieskorn modules
cites work: Q5820721
cites work: Petrov modules and zeros of abelian integrals
cites work: Q5757096
cites work: Q5421079
cites work: Q5601042
cites work: THE ORIGIN OF LIMIT CYCLES UNDER PERTURBATION OF THE EQUATIONdw/dz= -Rz/Rw, WHERER(z,w) IS A POLYNOMIAL
cites work: Q5588717
cites work: Q5630409
cites work: Modules of the Abelian integrals and the Picard$ndash$Fuchs systems*
cites work: Multidimensional generalization of the Il'yashenko theorem on abelian integrals
cites work: Critical values and the determinant of the periods
DOI: 10.5802/AIF.2204
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5145714