Reflection Vectors and Quantum Cohomology of Blowups
Let be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup Blₚₜ() of at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of Blₚₜ() is a reflectiongroup. We found explicit formulas for certain ge...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212166 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Reflection Vectors and Quantum Cohomology of Blowups. Todor Milanov and Xiaokun Xia. SIGMA 20 (2024), 029, 60 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862711025086758912 |
|---|---|
| author | Milanov, Todor Xia, Xiaokun |
| author_facet | Milanov, Todor Xia, Xiaokun |
| citation_txt | Reflection Vectors and Quantum Cohomology of Blowups. Todor Milanov and Xiaokun Xia. SIGMA 20 (2024), 029, 60 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup Blₚₜ() of at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of Blₚₜ() is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of Blpt() depending only on the geometry of the exceptional divisor.
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| first_indexed | 2026-03-19T14:26:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212166 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T14:26:22Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Milanov, Todor Xia, Xiaokun 2026-01-30T08:16:33Z 2024 Reflection Vectors and Quantum Cohomology of Blowups. Todor Milanov and Xiaokun Xia. SIGMA 20 (2024), 029, 60 pages 1815-0659 2020 Mathematics Subject Classification: 14N35; 35Q53 arXiv:2304.04365 https://nasplib.isofts.kiev.ua/handle/123456789/212166 https://doi.org/10.3842/SIGMA.2024.029 Let be a smooth projective variety with a semisimple quantum cohomology. It is known that the blowup Blₚₜ() of at one point also has semisimple quantum cohomology. In particular, the monodromy group of the quantum cohomology of Blₚₜ() is a reflectiongroup. We found explicit formulas for certain generators of the monodromy group of the quantum cohomology of Blpt() depending only on the geometry of the exceptional divisor. We would like to thank the anonymous referees for many useful suggestions that helped us improve the exposition. The research of T.M. is partially supported by Grant-in-Aid (Kiban C) 17K05193 and JP22K03265. This work is supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Reflection Vectors and Quantum Cohomology of Blowups Article published earlier |
| spellingShingle | Reflection Vectors and Quantum Cohomology of Blowups Milanov, Todor Xia, Xiaokun |
| title | Reflection Vectors and Quantum Cohomology of Blowups |
| title_full | Reflection Vectors and Quantum Cohomology of Blowups |
| title_fullStr | Reflection Vectors and Quantum Cohomology of Blowups |
| title_full_unstemmed | Reflection Vectors and Quantum Cohomology of Blowups |
| title_short | Reflection Vectors and Quantum Cohomology of Blowups |
| title_sort | reflection vectors and quantum cohomology of blowups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212166 |
| work_keys_str_mv | AT milanovtodor reflectionvectorsandquantumcohomologyofblowups AT xiaxiaokun reflectionvectorsandquantumcohomologyofblowups |