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dc.contributor.authorEdo, Eric
dc.contributor.authorEssen, Arno van den
dc.contributor.authorMaubach, Stefan
dc.date.accessioned2016-10-10T08:41:25Z
dc.date.available2016-10-10T08:41:25Z
dc.date.issued2008
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1222
dc.descriptionOWLF 2007en_US
dc.description.abstractWe prove that for a polynomial $f \in k[x, y, z]$ equivalent are: (1)$f$ is a $k[z]$-coordinate of $k[z][x,y]$, and (2) $k[x, y, z]/(f)\cong k^[2]$ and $f(x,y,a)$ is a coordinate in $k[x,y]$ for some $a \in k$. This solves a special case of the Abhyankar-Sathaye conjecture. As a consequence we see that a coordinate $f \in k[x,y,z]$ which is also a $k(z)$-coordinate, is a $k[z]$-coordinate. We discuss a method for constructing automorphisms of $k[x, y, z]$, and observe that the Nagata automorphism occurs naturally as the first non-trivial automorphism obtained by this method -essentially linking Nagata with a non-tame $R$-automorphism of $R[x]$, where $R=k[z]/(z^2)$.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2008,17
dc.titleA note on k[z]-Automorphisms in Two Variablesen_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-2008-17
local.scientificprogramOWLF 2007en_US
local.series.idOWP-2008-17
dc.identifier.urnurn:nbn:de:101:1-20081112144
dc.identifier.ppn1647467861


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