Buryak, A (2020) Extended r-spin theory and the mirror symmetry for the Ar–1-singularity. Moscow Mathematical Journal, 20 (3). pp. 475-493. ISSN 1609-4514
Abstract
By a famous result of K. Saito, the parameter space of the miniversal deformation of the Ar−1Ar−1 singularity carries a Frobenius manifold structure. The Landau–Ginzburg mirror symmetry says that, in the flat coordinates, the potential of this Frobenius manifold is equal to the generating series of certain integrals over the moduli space of rr spin curves. In this paper we show that the parameters of the miniversal deformation, considered as functions of the flat coordinates, also have a simple geometric interpretation using the extended rr spin theory, first considered by T. J. Jarvis, T. Kimura and A. Vaintrob, and studied in a recent paper of E. Clader, R. J. Tessler and the author. We prove a similar result for the singularity D4D4 and present conjectures for the singularities E6E6 and E8E8.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article is protected by copyright. Materials in this journal may be reproduced by any means for educational and scientific purposes without fee or permission (provided that the customary acknowledgment of the source is given). |
Keywords: | Moduli space of curves, Frobenius manifold, singularity, mirror symmetry |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Dec 2019 12:09 |
Last Modified: | 05 Jun 2020 02:40 |
Published Version: | http://www.mathjournals.org/mmj/2020-020-003/2020-... |
Status: | Published |
Publisher: | Independent University of Moscow |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:154238 |