Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Uwe Nagel
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.
Petrovic, Sonja, "ALGEBRAIC AND COMBINATORIAL PROPERTIES OF CERTAIN TORIC IDEALS IN THEORY AND APPLICATIONS" (2008). University of Kentucky Doctoral Dissertations. 606.