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 bibliographic references | eng |

dc.format.extent | iv, 45 pages | eng] |

dc.format.extent | iv, 45 pages | eng] |

dc.identifier.uri | https://hdl.handle.net/10355/66163 | |

dc.language | English | eng |

dc.publisher | University of Missouri--Columbia | eng |

dc.relation.ispartofcollection | 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 |