2021/01/25 by Daniel Barlet, Barlet, Daniel · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2101.09955
openalex publication_date 2021/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explain that in the study of the asymptotic expansion at the origin of a period integral like γz ω/df or of a hermitian period like f =s ρ.ω/df ∧ ω /df the computation of the Bernstein polynomial of the "fresco" (filtered differential equation) associated to the pair of germs (f, ω) 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 ω is a monomial holomorphic volume form. Several concrete examples are given.