Cavalieri, R., Johnson, P. orcid.org/0000-0002-6472-3000, Markwig, H. et al. (1 more author) (2021) Counting curves on Hirzebruch surfaces : tropical geometry and the Fock space. Mathematical Proceedings of the Cambridge Philosophical Society, 171 (1). pp. 165-205. ISSN 0305-0041
Abstract
We study the stationary descendant Gromov–Witten theory of toric surfaces by combining and extending a range of techniques – tropical curves, floor diagrams and Fock spaces. A correspondence theorem is established between tropical curves and descendant invariants on toric surfaces using maximal toric degenerations. An intermediate degeneration is then shown to give rise to floor diagrams, giving a geometric interpretation of this well-known bookkeeping tool in tropical geometry. In the process, we extend floor diagram techniques to include descendants in arbitrary genus. These floor diagrams are then used to connect tropical curve counting to the algebra of operators on the bosonic Fock space, and are showno coincide with the Feynman diagrams of appropriate operators. This extends work of a number of researchers, including Block–Göttsche, Cooper–Pandharipande and Block–Gathmann–Markwig.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 The Authors. This is an author-produced version of a paper subsequently published in Mathematical Proceedings of the Cambridge Philosophical Society. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 26 Oct 2021 10:27 |
Last Modified: | 26 Oct 2021 10:27 |
Status: | Published |
Publisher: | Cambridge University Press (CUP) |
Refereed: | Yes |
Identification Number: | 10.1017/s0305004120000171 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:179543 |