Hodge Diamonds of the Landau-Ginzburg Orbifolds
Consider the pairs (, ) with = (₁, …, ) being a polynomial defining a quasihomogeneous singularity and being a subgroup of SL(, ℂ), preserving . In particular, is not necessarily abelian. Assume further that contains the grading operator and satisfies the Calabi-Yau condition. We prove that th...
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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/123456789/212171 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Hodge Diamonds of the Landau-Ginzburg Orbifolds. Alexey Basalaev and Andrei Ionov. SIGMA 20 (2024), 024, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862572709915918336 |
|---|---|
| author | Basalaev, Alexey Ionov, Andrei |
| author_facet | Basalaev, Alexey Ionov, Andrei |
| citation_txt | Hodge Diamonds of the Landau-Ginzburg Orbifolds. Alexey Basalaev and Andrei Ionov. SIGMA 20 (2024), 024, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Consider the pairs (, ) with = (₁, …, ) being a polynomial defining a quasihomogeneous singularity and being a subgroup of SL(, ℂ), preserving . In particular, is not necessarily abelian. Assume further that contains the grading operator and satisfies the Calabi-Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of (, ) form a diamond. We identify its topmost, bottommost, leftmost, and rightmost entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms.
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| first_indexed | 2026-03-13T13:02:09Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-212171 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T13:02:09Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Basalaev, Alexey Ionov, Andrei 2026-01-30T08:18:39Z 2024 Hodge Diamonds of the Landau-Ginzburg Orbifolds. Alexey Basalaev and Andrei Ionov. SIGMA 20 (2024), 024, 25 pages 1815-0659 2020 Mathematics Subject Classification: 32S05; 14J33 arXiv:2307.01295 https://nasplib.isofts.kiev.ua/handle/123456789/212171 https://doi.org/10.3842/SIGMA.2024.024 Consider the pairs (, ) with = (₁, …, ) being a polynomial defining a quasihomogeneous singularity and being a subgroup of SL(, ℂ), preserving . In particular, is not necessarily abelian. Assume further that contains the grading operator and satisfies the Calabi-Yau condition. We prove that the nonvanishing bigraded pieces of the B-model state space of (, ) form a diamond. We identify its topmost, bottommost, leftmost, and rightmost entries as one-dimensional and show that this diamond enjoys the essential horizontal and vertical isomorphisms. The work of Alexey Basalaev was supported by the International Laboratory of Cluster Geometry NRU HSE, RF Government grant, ag. no.075-15-2021-608 dated 08.06.2021. The authors are grateful to Anton Rarovsky for sharing the pictures from his bachelor's thesis. The authors are very grateful to the anonymous referees for many valuable comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hodge Diamonds of the Landau-Ginzburg Orbifolds Article published earlier |
| spellingShingle | Hodge Diamonds of the Landau-Ginzburg Orbifolds Basalaev, Alexey Ionov, Andrei |
| title | Hodge Diamonds of the Landau-Ginzburg Orbifolds |
| title_full | Hodge Diamonds of the Landau-Ginzburg Orbifolds |
| title_fullStr | Hodge Diamonds of the Landau-Ginzburg Orbifolds |
| title_full_unstemmed | Hodge Diamonds of the Landau-Ginzburg Orbifolds |
| title_short | Hodge Diamonds of the Landau-Ginzburg Orbifolds |
| title_sort | hodge diamonds of the landau-ginzburg orbifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212171 |
| work_keys_str_mv | AT basalaevalexey hodgediamondsofthelandauginzburgorbifolds AT ionovandrei hodgediamondsofthelandauginzburgorbifolds |