Polydegree properties of polynomial automorphisms

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dc.contributor Dixon, Martyn R.
dc.contributor Evans, Martin J.
dc.contributor Corson, Jon M.
dc.contributor Borie, Richard B.
dc.contributor.advisor Lewis, Drew
dc.contributor.author Perry, Kaitlyn Anne
dc.date.accessioned 2017-03-01T17:40:25Z
dc.date.available 2017-03-01T17:40:25Z
dc.date.issued 2016
dc.identifier.other u0015_0000001_0002229
dc.identifier.other Perry_alatus_0004D_12680
dc.identifier.uri https://ir.ua.edu/handle/123456789/2587
dc.description Electronic Thesis or Dissertation
dc.description.abstract The group of automorphisms of the affine plane has the structure of an amalgamated free product of the triangular and affine subgroups. This leads us to the polydegree: the unique sequence of degrees of the triangular automorphisms in the amalgamated free product decomposition of the automorphism. This group is also endowed with the structure of an infinite dimensional algebraic variety. The interaction between these two structures is not well understood. We use the Valuation Criterion, due to Furter, to study the interaction between these structures; in particular, it allows us to see if an automorphism in G is also in the closure of $G_d$, where d is the polydegree sequence. In this paper, we will discuss a method that gives us new results concerning a class of automorphisms with a polydegree of length one being contained in the closure (in the Zariski topology) of a set of automorphisms with a polydegree of length 2.
dc.format.extent 57 p.
dc.format.medium electronic
dc.format.mimetype application/pdf
dc.language English
dc.language.iso en_US
dc.publisher University of Alabama Libraries
dc.relation.ispartof The University of Alabama Electronic Theses and Dissertations
dc.relation.ispartof The University of Alabama Libraries Digital Collections
dc.relation.hasversion born digital
dc.rights All rights reserved by the author unless otherwise indicated.
dc.subject.other Mathematics
dc.title Polydegree properties of polynomial automorphisms
dc.type thesis
dc.type text
etdms.degree.department University of Alabama. Dept. of Mathematics
etdms.degree.discipline Mathematics
etdms.degree.grantor The University of Alabama
etdms.degree.level doctoral
etdms.degree.name Ph.D.


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