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dc.contributor.authorNguyen, Hong Duc
dc.date.accessioned2016-09-22T10:46:36Z
dc.date.available2016-09-22T10:46:36Z
dc.date.issued2015-11-18
dc.identifier.urihttp://publications.mfo.de/handle/mfo/192
dc.descriptionOWLF 2015en_US
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 w.r.t. right equivalence. The classification of right simple singularities in 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. Moreover we completely determine all possible adjacency diagrams of simple,unimodal and bimodal singularities. 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. In contrast to the complex analytic case, there are, for any positive characteristic, only finitely many 1-dimensional (resp. 2-dimensional) families of right class of unimodal (resp. bimodal) singularities. We show that for fixed characteristic $p > 0 $ of the ground field, the Milnor number of f satisfies $\mu(f)<4p$, if the right modality of $f$ is at most 2.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2015,14
dc.titleRight Unimodal and Bimodal Singularities in Positive Characteristicen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2015-14
local.scientificprogramOWLF 2015
local.series.idOWP-2015-14
dc.identifier.urnurn:nbn:de:101:1-201511175694
dc.identifier.ppn1658875702


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