@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-tel-00875930v1> a dcat:Dataset ;
    dct:description """
              There are two parts in the present work. The first part concerns the asymptotic set of a polynomial mapping $F: \\C^n \\to \\C^n$. In the 90s, Zbigniew Jelonek showed that this set is a $(n-1)$ - (complex) dimensional singular variety. We gave a method, called méthode façon, for stratifying this set. We obtained a Thom-Mather stratification. Moreover, there exists a Whitney stratification such that the set of possible façons is constant on every stratum. By using the façons, we gave an algorithm for expliciting the asymptotic sets of a dominant quadratic polynomial mapping in three variables. As a result, we have a complete list of the asymptotic sets in this case. The second part concerns the set called Valette set $V_F$. In 2010, Anna and Guillaume Valette constructed a real pseudomanifold $V_F \\subset \\R^{2n + p}$, where $p > 0$, associated to a polynomial mapping $F: \\C^n \\to \\C^n$. In the case $n = 2$, they proved that if $F$ is a polynomial mapping with nowhere vanishing Jacobian, then $F$ is not proper if and only if the homology (or intersection homology) of $V_F$ is not trivial in dimension 2. We gave a generalization of this result, in the case of a polynomial mapping $F = (F_1, \\ldots, F_n): \\C^n \\to \\C^n$ with nowhere vanishing Jacobian. We gave also a method for stratifying the set $V_F$. As applications, we have the stratifications of the set $K_{\\infty}(F)$ of asymptotic critial values of $F$, the set $B(F)$ of bifurcation points of $F$.
            """ ;
    dct:identifier "tel-00875930" ;
    dct:issued "2026-05-09T06:51:10.482775"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-09T06:51:10.482779"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Study of somes singular sets associated to a polynomial map" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00875930v1/resource/48d06804-4152-442c-a8f6-01e205ae3d0b> ;
    dcat:keyword "application-polynomiale",
        "asymptotic-set",
        "ensemble-asymptotique",
        "infoeu-reposemanticsdoctoralthesis",
        "mathmath-agmathematics-mathalgebraic-geometry-mathag",
        "polynomial-mapping",
        "singularities",
        "stratification",
        "theses" ;
    dcat:landingPage <https://theses.hal.science/tel-00875930> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00875930v1/resource/48d06804-4152-442c-a8f6-01e205ae3d0b> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-09T06:51:10.484747"^^xsd:dateTime ;
    dct:modified "2026-05-09T06:51:10.467809"^^xsd:dateTime ;
    dct:title "Study of somes singular sets associated to a polynomial map" ;
    dcat:accessURL <https://theses.hal.science/tel-00875930> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://theses.hal.science/tel-00875930> a foaf:Document .