Lutz, Wendelin;
(2022)
On Gromov-Witten invariants of blowups and the classification of T-polygons.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
I prove a Torelli theorem for certain Laurent polynomials. This provides strong evidence for the idea that, under mirror symmetry, a Fano manifold corresponds to a single geometric object called a cluster variety. As things stand, mirror symmetry provides a one-to-many correspondence between a single Fano manifold and a collection of Laurent polynomials (or Landau--Ginzburg models); my result gives a geometric proof that, for smooth Fanos in dimension two, these Laurent polynomials assemble to give a single cluster variety. My other theorem is joint work with Tom Coates and Qaasim Shafi, and determines, under mild hypotheses, how the genus-zero Gromov--Witten invariants of a space X change under blow-ups of X. This is a significant result in enumerative geometry; it also expands the range of Fano manifolds for which we can establish mirror symmetry.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | On Gromov-Witten invariants of blowups and the classification of T-polygons |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10153706 |
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