@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00783046v1> a dcat:Dataset ;
    dct:description """
              In this paper we introduce the word {\\em fresco} to denote a monogenic geometric (a,b)-module. This "basic object" (generalized Brieskorn module with one generator) corresponds to the formal germ of the minimal filtered (regular) differential equation. Such an equation is satisfied by a relative de Rham cohomology class at a critical value of a holomorphic function on a smooth complex manifold. In [B.09] the first structure theorems are proved. Then in [B.10] we introduced the notion of {\\em theme} which corresponds in the \\ $[\\lambda]-$primitive case to frescos having a unique Jordan-H{ö}lder sequence (a unique Jordan block for the monodromy). Themes correspond to asymptotic expansion of a given vanishing period, so to an image of a fresco in the module of asymptotic expansions. For a fixed relative de Rham cohomology class (for instance given by a smooth differential form $d-$closed and $df-$closed) each choice of a vanishing cycle in the spectral eigenspace of the monodromy for the eigenvalue \\ $exp(2i\\pi.\\lambda)$ \\ produces a \\ $[\\lambda]-$primitive theme, which is a quotient of the fresco associated to the given relative de Rham class itself. \\\\ We show that for any fresco there exists an {\\em unique} Jordan-H{ö}lder sequence, called the {\\em principal J-H. sequence}, with corresponding quotients giving the opposite of the roots of the Bernstein polynomial in increasing order. We study the semi-simple part of a given fresco and we characterize the semi-simplicity of a fresco by the fact for any given order on the roots of its Bernstein polynomial we may find a J-H. sequence making them appear with this order. Then we construct a numerical invariant, called the \\ $\\beta-$invariant, and we show that it produces numerical criteria in order to give a necessary and sufficient condition on a fresco to be semi-simple. We show that these numerical invariants define a natural algebraic stratification on the set of isomorphism classes of fresco with given fundamental invariants (or equivalently with given roots of the Bernstein polynomial).
            """ ;
    dct:identifier "hal-00783046" ;
    dct:issued "2026-05-14T19:24:28.836742"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-14T19:24:28.836751"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Asymptotics of a vanishing period : characterization of semi-simplicity" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00783046v1/resource/1c2e3ec0-4eee-48a6-913f-4c91d6e60107> ;
    dcat:keyword "a_",
        "asymptotic-expansion",
        "b-module",
        "bernstein-polynomial",
        "brieskorn-module",
        "filtered-differential-equation",
        "fresco",
        "gauss-manin-connection",
        "infoeu-reposemanticspreprint",
        "mathmath-agmathematics-mathalgebraic-geometry-mathag",
        "mathmath-cvmathematics-mathcomplex-variables-mathcv",
        "msc--32-s-25--32-s-40--32-s-50",
        "preprints-working-papers-",
        "theme",
        "vanishing-period" ;
    dcat:landingPage <https://hal.science/hal-00783046> .

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    dct:issued "2026-05-14T19:24:28.842562"^^xsd:dateTime ;
    dct:modified "2026-05-14T19:24:28.792394"^^xsd:dateTime ;
    dct:title "Asymptotics of a vanishing period : characterization of semi-simplicity" ;
    dcat:accessURL <https://hal.science/hal-00783046> .

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