Modular forms in enumerative geometry
Abstract/Contents
- Abstract
- Let X be an elliptically fibered Calabi-Yau threefold given by a very general Weierstrass equation over the projective plane. In this thesis, we answer the enumerative question of how many smooth rational curves lie on X over lines in the base plane, proving part of a conjecture by Huang, Katz, and Klemm. The key inputs are a modularity theorem of Kudla and Millson for locally symmetric spaces of orthogonal type and the deformation theory of A-D-E singularities.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Greer, François |
|---|---|
| Associated with | Stanford University, Department of Mathematics. |
| Primary advisor | Li, Jun, (Mathematician) |
| Thesis advisor | Li, Jun, (Mathematician) |
| Thesis advisor | Ionel, Eleny |
| Thesis advisor | Vakil, Ravi |
| Advisor | Ionel, Eleny |
| Advisor | Vakil, Ravi |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | François Greer. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Francois William Greer
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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