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Abstract
We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial xr. Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (ℂ, xr) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22].
| Original language | English |
|---|---|
| Pages (from-to) | 1005–1024 |
| Number of pages | 20 |
| Journal | Pure and Applied Mathematics Quarterly |
| Volume | 20 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 3 Apr 2024 |
Bibliographical note
Acknowledgments:The authors would like to thank Alexander Buryak and Robert Maher for discussions relating to this work. The first author acknowledges support from the EPSRC under Grants EP/N03189X/1, a Royal Society Wolfson Research Merit Award, and the ERC Advanced Grant MSAG. The second author acknowledges that this paper is based upon work supported by the UKRI and EPSRC under fellowships MR/T01783X/1 and EP/N004922/2. The third author, incumbent of the Lillian and George Lyttle Career Development Chair, acknowledges support provided by the ISF grant No. 335/19 and by a research grant from the Center for New Scientists of Weizmann Institute. We thank the referee for their useful comments that have improved the paper.
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Open Mirror Geometry for Landau-Ginzburg Models
Kelly, T. (Principal Investigator)
1/11/20 → 30/06/25
Project: Research Councils
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Bridging Frameworks via Mirror Symmetry
Kelly, T. (Principal Investigator)
Engineering & Physical Science Research Council
1/09/18 → 31/08/19
Project: Research Councils