Algebraic differential equations of periods integrals
arXiv:2101.09955
Abstract
We explain that in the study of the asymptotic expansion at the origin of a period integral like z /df or of a hermitian period like f =s ./df /df the computation of the Bernstein polynomial of the "fresco" (filtered differential equation) associated to the pair of germs (f, ) gives a better control than the computation of the Bernstein polynomial of the full Brieskorn module of the germ of f at the origin. Moreover, it is easier to compute as it has a better functoriality and smaller degree. We illustrate this in the case where f C[x 0 ,. .. , x n ] has n + 2 monomials and is not quasi-homogeneous, by giving an explicite simple algorithm to produce a multiple of the Bernstein polynomial when is a monomial holomorphic volume form. Several concrete examples are given.
Le cas de la version pr{é}c{é}dente est vide !