An explicit formula for period determinant
Annales de l'Institut Fourier, Volume 56 (2006) no. 4, p. 887-917

We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.

Nous considérons un polynôme générique à deux variables complexes et une base de cycles dans le premier groupe d’homologie d’une courbe de niveau non singulière. Nous prenons une collection arbitraire de 1-formes polynomiales homogènes de degrés appropriés, de sorte que leurs intégrales le long des cycles de la base forment une matrice carrée (de fonctions multivaluées en la valeur du niveau). Nous calculons le déterminant de cette matrice.

DOI : https://doi.org/10.5802/aif.2204
Classification:  14D05,  32S10,  32S20
Keywords: Complex polynomial in two variables, homology of nonsingular level curve, monodromy, abelian integral, gradient ideal, period determinant
@article{AIF_2006__56_4_887_0,
     author = {Glutsyuk, Alexey A.},
     title = {An explicit formula for period~determinant},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {56},
     number = {4},
     year = {2006},
     pages = {887-917},
     doi = {10.5802/aif.2204},
     mrnumber = {2266882},
     zbl = {1140.32011},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2006__56_4_887_0}
}
Glutsyuk, Alexey A. An explicit formula for period determinant. Annales de l'Institut Fourier, Volume 56 (2006) no. 4, pp. 887-917. doi : 10.5802/aif.2204. http://www.numdam.org/item/AIF_2006__56_4_887_0/

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