Homological mirror symmetry for elliptic Hopf surfaces
Abstract/Contents
- Abstract
- We define the notion of a non-algebraic Landau-Ginzburg model and its associated Fukaya category. We show that non-Kahler surfaces obtained by performing two logarithmic transformations to the product of the projective line and an elliptic curve have non-algebraic Landau-Ginzburg models as their mirror spaces in the sense of homological mirror symmetry. This class of surface includes the classical Hopf surface and other elliptic primary and secondary Hopf surfaces. We also define localization maps from the Fukaya categories associated to the Landau-Ginzburg models to partially wrapped and fully wrapped categories, and we show mirror symmetry results that relate the partially wrapped and fully wrapped categories to spaces of coherent analytic sheaves on open submanifolds of the compact complex surfaces in question. We use these results to sketch a proof of a full homological mirror symmetry result for these compact surfaces
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2020; ©2020 |
| Publication date | 2020; 2020 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Ward, Abigail Rose |
|---|---|
| Degree supervisor | Auroux, Denis |
| Degree supervisor | Vakil, Ravi |
| Thesis advisor | Auroux, Denis |
| Thesis advisor | Vakil, Ravi |
| Thesis advisor | Eliashberg, Y, 1946- |
| Degree committee member | Eliashberg, Y, 1946- |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Abigail Ward |
|---|---|
| Note | Submitted to the Department of Mathematics |
| Thesis | Thesis Ph.D. Stanford University 2020 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2020 by Abigail Rose Ward
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...