1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ²
Using the inverse period map of the Gauss-Manin connection associated with *(ℂℙ²) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin-Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of ℂℙ². In the case of small qu...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213177 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 1D Landau-Ginzburg Superpotential of Big Quantum Cohomology of ℂℙ². Guilherme F. Almeida. SIGMA 21 (2025), 038, 65 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Using the inverse period map of the Gauss-Manin connection associated with *(ℂℙ²) and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin-Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of ℂℙ². In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the -invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of *(ℂℙ²) in closed form as the composition of the Weierstrass ℘-function and the universal coverings of ℂ∖(ℤ⊕eπⁱᐟ³ℤ) and ℂ∖(ℤ⊕ℤ), respectively.
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| ISSN: | 1815-0659 |