Degree Year
2011
Document Type
Thesis - Open Access
Degree Name
Bachelor of Arts
Department
Mathematics
Advisor(s)
Kevin Woods
Keywords
Toric algebra, Normal toric varieties, Triangulations, Normal configurations, &916, -normal configurations, Unimodular, Unimodular triangulations, Unimodular coverings, Toric ideals, Regular unimodular triangulations
Abstract
Toric algebra is a field of study that lies at the intersection of algebra, geometry, and combinatorics. Thus, the algebraic properties of the toric ideal IA defined by the vector configuration A are often characterizable via the geometric and combinatorial properties of its corresponding toric variety and A, respectively. Here, we focus on the property of normality of A. A normal vector configuration defines the toric ideal of a normal toric variety. However, the definition of normality of A is based entirely on the algebraic structures associated with A without regard to any of its combinatorial properties. In this paper, we discuss two attempts to provide a combinatorial characterization of normality of A. Particularly, we show that the properties "the convex hull of A possesses a unimodular covering" and "A is a Δ-normal configuration" are both sufficient conditions for normality of A, but neither is necessary. This suggests that another combinatorial property is required to provide the desired characterization of normality of A.
Repository Citation
Solus, Liam, "Normal and Δ-Normal Configurations in Toric Algebra" (2011). Honors Papers. 424.
https://digitalcommons.oberlin.edu/honors/424
