dc.contributor.advisor | Cutkosky, Dale | eng |
dc.contributor.author | Dutta, Arpan | eng |
dc.date.issued | 2018 | eng |
dc.date.submitted | 2018 Spring | eng |
dc.description.abstract | In this thesis we develop a method for constructing generating sequences for valuations dominating the ring of a two dimensional quotient singularity. Suppose that K is an algebraically closed field of characteristic zero, K[X, Y] is a polynomial ring over K and v is a rational rank 1 valuation of the field K(X, Y) which dominates K[X, Y](X,Y) . Given a finite Abelian group H acting diagonally on K[X, Y], and a generating sequence of v in K[X, Y] whose members are eigenfunctions for the action of H, we compute a generating sequence for the invariant ring K[X, Y]H. We use this to compute the semigroup SK[X,Y ]H (v) of values of elements of K[X, Y]H. We further determine when SK[X,Y ]H (v) is a finitely generated SK[X,Y ]H (v)-module. | eng |
dc.description.bibref | Includes bibliographical references. | eng |
dc.format.extent | iv, 45 pages | eng |
dc.identifier.uri | https://hdl.handle.net/10355/66163 | |
dc.identifier.uri | https://doi.org/10.32469/10355/66163 | eng |
dc.language | English | eng |
dc.publisher | University of Missouri--Columbia | eng |
dc.relation.ispartofcommunity | University of Missouri--Columbia. Graduate School. Theses and Dissertations | eng |
dc.rights | OpenAccess. | eng |
dc.rights.license | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. | eng |
dc.title | Generating sequences and semigroups of valuations on 2 dimensional normal local rings | eng |
dc.type | Thesis | eng |
thesis.degree.discipline | Mathematics (MU) | eng |
thesis.degree.grantor | University of Missouri--Columbia | eng |
thesis.degree.level | Doctoral | eng |
thesis.degree.name | Ph. D. | eng |