Local Moduli of Semisimple Frobenius Coalescent Structures
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities, and mutual constraints are allowed in the definition of monodromy data, in view of their importan...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210710 |
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| Cite this: | Local Moduli of Semisimple Frobenius Coalescent Structures. Giordano Cotti, Boris Dubrovin and Davide Guzzetti. SIGMA 16 (2020), 040, 105 pages |
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Cotti, Giordano Dubrovin, Boris Guzzetti, Davide 2025-12-15T15:26:46Z 2020 Local Moduli of Semisimple Frobenius Coalescent Structures. Giordano Cotti, Boris Dubrovin and Davide Guzzetti. SIGMA 16 (2020), 040, 105 pages 1815-0659 2020 Mathematics Subject Classification: 34M56;53D45;18E30 arXiv:1712.08575 https://nasplib.isofts.kiev.ua/handle/123456789/210710 https://doi.org/10.3842/SIGMA.2020.040 We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities, and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural relationships between Frobenius manifolds and derived categories. Detailed examples and applications are taken from singularity and quantum cohomology theories. We explicitly compute the monodromy data at points of the Maxwell Stratum of the A₃-Frobenius manifold, as well as at the small quantum cohomology of the Grassmannian 𝔾₂(ℂ⁴). In the latter case, we analyse in detail the action of the braid group on the monodromy data. This proves that these data can be expressed in terms of characteristic classes of mutations of Kapranov's exceptional 5-block collection, as conjectured by one of the authors. We would like to thank Marco Bertola, Ugo Bruzzo, Barbara Fantechi, Claus Hertling, Claude Sabbah, Maxim Smirnov, Jacopo Stoppa, Ian Strachan, and Di Yang for several discussions and helpful comments. We would also like to thank the anonymous referees, whose valuable comments have improved the paper. The first author is grateful to the Max-Planck Institut fur Mathematik in Bonn for hospitality and support. The third author is a member of the European Union's H2020 research and innovation programme under the Marie Sklodowska-Curie grant No. 778010 IPaDEGAN. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Local Moduli of Semisimple Frobenius Coalescent Structures Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Local Moduli of Semisimple Frobenius Coalescent Structures |
| spellingShingle |
Local Moduli of Semisimple Frobenius Coalescent Structures Cotti, Giordano Dubrovin, Boris Guzzetti, Davide |
| title_short |
Local Moduli of Semisimple Frobenius Coalescent Structures |
| title_full |
Local Moduli of Semisimple Frobenius Coalescent Structures |
| title_fullStr |
Local Moduli of Semisimple Frobenius Coalescent Structures |
| title_full_unstemmed |
Local Moduli of Semisimple Frobenius Coalescent Structures |
| title_sort |
local moduli of semisimple frobenius coalescent structures |
| author |
Cotti, Giordano Dubrovin, Boris Guzzetti, Davide |
| author_facet |
Cotti, Giordano Dubrovin, Boris Guzzetti, Davide |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We extend the analytic theory of Frobenius manifolds to semisimple points with coalescing eigenvalues of the operator of multiplication by the Euler vector field. We clarify which freedoms, ambiguities, and mutual constraints are allowed in the definition of monodromy data, in view of their importance for conjectural relationships between Frobenius manifolds and derived categories. Detailed examples and applications are taken from singularity and quantum cohomology theories. We explicitly compute the monodromy data at points of the Maxwell Stratum of the A₃-Frobenius manifold, as well as at the small quantum cohomology of the Grassmannian 𝔾₂(ℂ⁴). In the latter case, we analyse in detail the action of the braid group on the monodromy data. This proves that these data can be expressed in terms of characteristic classes of mutations of Kapranov's exceptional 5-block collection, as conjectured by one of the authors.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210710 |
| citation_txt |
Local Moduli of Semisimple Frobenius Coalescent Structures. Giordano Cotti, Boris Dubrovin and Davide Guzzetti. SIGMA 16 (2020), 040, 105 pages |
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| first_indexed |
2025-12-17T12:04:33Z |
| last_indexed |
2025-12-17T12:04:33Z |
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1851756981440741376 |