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Gopakumar-Vafa invariants of Banana type manifolds Morishige, Nina
Abstract
This research develops a method to compute Katz's genus 0 Gopakumar-Vafa invariants of fiber curve classes of the Banana manifold, a smooth compact Calabi-Yau threefold, and its generalizations, the multi-Banana configurations. The invariants turn out to have geometric significance, being an actual count of certain local configurations of rational curves on a related threefold. In both these cases, the partition functions for the invariants exhibit a modularity and can be expressed in terms of Jacobi forms or theta functions.
Item Metadata
| Title | Gopakumar-Vafa invariants of Banana type manifolds |
| Creator | Morishige, Nina |
| Publisher | University of British Columbia |
| Date Issued | 2021 |
| Description |
This research develops a method to compute Katz's genus 0 Gopakumar-Vafa invariants of fiber curve classes of the Banana manifold, a smooth compact Calabi-Yau threefold, and its generalizations, the multi-Banana configurations. The invariants turn out to have geometric significance, being an actual count of certain local configurations of rational curves on a related threefold. In both these cases, the partition functions for the invariants exhibit a modularity and can be expressed in terms of Jacobi forms or theta functions.
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| Genre | Thesis/Dissertation |
| Type | Text |
| Language | eng |
| Date Available | 2021-07-20 |
| Provider | Vancouver : University of British Columbia Library |
| Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
| DOI | 10.14288/1.0400498 |
| URI | |
| Degree | Doctor of Philosophy - PhD |
| Program | Mathematics |
| Affiliation | Science, Faculty of; Mathematics, Department of |
| Degree Grantor | University of British Columbia |
| Graduation Date | 2021-11 |
| Campus | UBCV |
| Scholarly Level | Graduate |
| Rights URI | |
| Aggregated Source Repository | DSpace |
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Attribution-NonCommercial-NoDerivatives 4.0 International