ALGEBRAIC AND COMBINATORIAL PROPERTIES OF CERTAIN TORIC IDEALS IN THEORY AND APPLICATIONS

Author

Sonja Petrovic, University of KentuckyFollow

Date Available

12-14-2011

Year of Publication

2008

Degree Name

Doctor of Philosophy (PhD)

Document Type

Dissertation

College

Arts and Sciences

Department

Mathematics

First Advisor

Dr. Uwe Nagel

Abstract

This work focuses on commutative algebra, its combinatorial and computational aspects, and its interactions with statistics. The main objects of interest are projective varieties in Pⁿ, algebraic properties of their coordinate rings, and the combinatorial invariants, such as Hilbert series and Gröbner fans, of their defining ideals. Specifically, the ideals in this work are all toric ideals, and they come in three flavors: they are defining ideals of a family of classical varieties called rational normal scrolls, cut ideals that can be associated to a graph, and phylogenetic ideals arising in a new and increasingly popular area of algebraic statistics.

Recommended Citation

Petrovic, Sonja, "ALGEBRAIC AND COMBINATORIAL PROPERTIES OF CERTAIN TORIC IDEALS IN THEORY AND APPLICATIONS" (2008). University of Kentucky Doctoral Dissertations. 606.
https://uknowledge.uky.edu/gradschool_diss/606