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Normal and Δ-Normal Configurations in Toric Algebra

Solus, Liam
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1308243895

Abstract Details

2011, BA, Oberlin College, Mathematics.
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.
Kevin Woods, PhD (Advisor)
27 p.
Mathematics
toric algebra; normal toric varieties; triangulations; normal configurations; &916; -normal configurations; unimodular; unimodular triangulations; unimodular coverings; toric ideals; regular unimodular triangulations

Recommended Citations

Citations

  • Solus, L. (2011). Normal and Δ-Normal Configurations in Toric Algebra [Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1308243895

    APA Style (7th edition)

  • Solus, Liam. Normal and Δ-Normal Configurations in Toric Algebra. 2011. Oberlin College, Undergraduate thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1308243895.

    MLA Style (8th edition)

  • Solus, Liam. "Normal and Δ-Normal Configurations in Toric Algebra." Undergraduate thesis, Oberlin College, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1308243895

    Chicago Manual of Style (17th edition)

oberlin1308243895
576
© 2011, all rights reserved.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.