An explicit formula for period determinant  [ Formule pour déterminant de périodes ]
Annales de l'Institut Fourier, Tome 56 (2006) no. 4, pp. 887-917.

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.

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.

Reçu le : 2005-07-19
Accepté le : 2005-11-21
DOI : https://doi.org/10.5802/aif.2204
Classification : 14D05,  32S10,  32S20
Mots clés: Polynôme complexe à deux variables, homologie d’une courbe de niveau non singulière, monodromie, intégrale abélienne, idéal du gradient, déterminant de périodes
@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},
     zbl = {1140.32011},
     mrnumber = {2266882},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2006__56_4_887_0/}
}
Glutsyuk, Alexey A. An explicit formula for period determinant. Annales de l'Institut Fourier, Tome 56 (2006) no. 4, pp. 887-917. doi : 10.5802/aif.2204. https://aif.centre-mersenne.org/item/AIF_2006__56_4_887_0/

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