dc.contributor.author Nguyen, H.D. dc.date.accessioned 2018-11-09T10:03:05Z dc.date.available 2018-11-09T10:03:05Z dc.date.issued 2017-08-07 dc.identifier.issn 1073-7928 dc.identifier.uri http://hdl.handle.net/20.500.11824/887 dc.description.abstract The 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.sponsorship IJCI-2016-29891 en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Classification of singularities, Modality, Normal forms en_US dc.title Right unimodal and bimodal singularities in positive characteristic en_US dc.type info:eu-repo/semantics/doctoralThesis en_US dc.identifier.doi 10.1093/imrn/rnx165 dc.relation.publisherversion https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnx165/4071001?redirectedFrom=fulltext en_US dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title International Mathematics Research Notices en_US
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