dc.contributor.author Nguyen, Hong Duc dc.date.accessioned 2016-09-22T10:46:36Z dc.date.available 2016-09-22T10:46:36Z dc.date.issued 2015-11-18 dc.identifier.uri http://publications.mfo.de/handle/mfo/192 dc.description OWLF 2015 en_US 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 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.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2015,14 dc.title Right Unimodal and Bimodal Singularities in Positive Characteristic en_US dc.type Preprint en_US dc.rights.license Dieses 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.license This 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.doi 10.14760/OWP-2015-14 local.scientificprogram OWLF 2015 local.series.id OWP-2015-14 dc.identifier.urn urn:nbn:de:101:1-201511175694 dc.identifier.ppn 1658875702
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