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dc.contributor.authorNguyen, H.D.
dc.date.accessioned2018-11-09T10:03:05Z
dc.date.available2018-11-09T10:03:05Z
dc.date.issued2017-08-07
dc.identifier.issn1073-7928
dc.identifier.urihttp://hdl.handle.net/20.500.11824/887
dc.description.abstractThe problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple singularities positive characteristic was achieved by Greuel and the author in 2014. In the present paper we classify right unimodal and bimodal singularities in positive characteristic by giving explicit normal forms. It is surprising that in positive characteristic, there are no infinite series of unimodal and bimodal singularities. Moreover, the Milnor number of simple, unimodal and bimodal singularity satisfies $\mu(f)\leq 4p$. As an application we prove that, for singularities of right modality at most 2, the $\mu$-constant stratum is smooth and its dimension is equal to the right modality.en_US
dc.description.sponsorshipIJCI-2016-29891en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectClassification of singularities, Modality, Normal formsen_US
dc.titleRight unimodal and bimodal singularities in positive characteristicen_US
dc.typeinfo:eu-repo/semantics/doctoralThesisen_US
dc.identifier.doi10.1093/imrn/rnx165
dc.relation.publisherversionhttps://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnx165/4071001?redirectedFrom=fulltexten_US
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/FP7/615655en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleInternational Mathematics Research Noticesen_US


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