Generating sequences and semigroups of valuations on 2 dimensional normal local rings

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics (MU)

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2018

Author dc:creator

• Dutta, Arpan

Advisor dc:contributor.advisor

• Cutkosky, Dale

Statement dc:rights

• OpenAccess.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.32469/10355/66163

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/66163