Graduation Year

2025

Date of Submission

12-2024

Document Type

Campus Only Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematical Sciences

Reader 1

Reginald Anderson

Abstract

This paper describes work done to explore the topic of smooth projective toric Fano 4-folds that possess a full strong exceptional collection of line bundles. In previous work done over the summer of 2024, we found that 72/124 of the smooth toric Fano 4-folds possess a full strong exceptional collection of line bundles. We use data from the polymake database, which lists a classification of smooth reflexive lattice Fano polytopes in the first nine dimensions. In addition to getting the ratio of 72/124, we also wanted to check Bondal's numerical criterion to figure out why the other 4-folds did not possess a full strong exceptional collection of line bundles. We were able to find that the passing and failing of Bondal's numerical criterion coincided directly with the possession of a full strong exceptional collection of line bundles.

This thesis is restricted to the Claremont Colleges current faculty, students, and staff.

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