#### Degree Year

2011

#### Document Type

Thesis

#### 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