|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
The
quantum tropical vertex
Pierrick Bousseau |
|
Geometry & Topology 24 (2020) 1297–1379
|
Abstract |
|
Gross, Pandharipande and Siebert have shown that the –dimensional Kontsevich–Soibelman scattering diagrams compute certain genus-zero log Gromov–Witten invariants of log Calabi–Yau surfaces. We show that the –refined –dimensional Kontsevich–Soibelman scattering diagrams compute, after the change of variables , generating series of certain higher-genus log Gromov–Witten invariants of log Calabi–Yau surfaces. This result provides a mathematically rigorous realization of the physical derivation of the refined wall-crossing formula from topological string theory proposed by Cecotti and Vafa and, in particular, can be viewed as a nontrivial mathematical check of the connection suggested by Witten between higher-genus open A–model and Chern–Simons theory. We also prove some new BPS integrality results and propose some other BPS integrality conjectures. |
PDF Access Denied
We have not been able to recognize your IP address
18.97.9.168
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for USD 40.00:
Keywords
scattering diagrams, quantum tori, Gromov–Witten invariants
|
Mathematical Subject Classification 2010
Primary: 14N35
|
References |
Publication
Received: 15 November 2018
Revised: 1 July 2019
Accepted: 4 September 2019
Published: 30 September 2020
Proposed: Jim Bryan
Seconded: Dan Abramovich, Richard P Thomas
|
Authors |
| Pierrick Bousseau | |
| Department of Mathematics Imperial College London London United Kingdom |
Institute for Theoretical
Studies ETH Zürich Zürich Switzerland |
