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
Date:2024
Main Authors: Milanov, Todor, Xia, Xiaokun
Format: Article
Language:English
Published: Інститут математики НАН України 2024
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
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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.
first_indexed 2026-03-19T14:26:22Z
format Article
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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.
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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