Date Approved

7-15-2015

Date Posted

6-22-2016

Degree Type

Open Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Committee Member

Andrew Wilfong, Ph.D., Chair

Committee Member

David Folk, Ph.D.

Committee Member

Jayakumar Ramanathan, Ph.D.

Abstract

The number theoretic conjecture we examine in this paper originates when trying to construct a characterizable generating set for the complex cobordism polynomial ring. To date there is no efficient, universal method for characterizing such a generating set. Wilfong conjectures that smooth projective toric varieties can act as these generators [7]. Toric varieties are related to polytopes by a bijective correspondence. Studying the combinatorial structure of these polytopes is much more manageable than studying properties of toric varieties directly. This gives rise to the number theoretic conjecture considered here. A proof of this number theoretic conjecture would in turn prove the conjecture that smooth projective toric varieties provide a generating set for the complex cobordism polynomial ring. Here, we do not provide a complete proof of the number theoretic conjecture, rather we give more evidence to the conjecture, building on prior work of Wilfong and Parry.

Included in

Mathematics Commons

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