Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0
We extract genus 0 consequences of the all genera quantum HRR formula proved in Part IX. This includes re-proving and generalizing the adelic characterization of genus 0 quantum K-theory found in [Givental A., Tonita V., in Symplectic, Poisson, and Noncommutative Geometry, Math. Sci. Res. Inst. Publ...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210719 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0. Alexander Givental. SIGMA 16 (2020), 031, 16 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730997714386944 |
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| author | Givental, Alexander |
| author_facet | Givental, Alexander |
| citation_txt | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0. Alexander Givental. SIGMA 16 (2020), 031, 16 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We extract genus 0 consequences of the all genera quantum HRR formula proved in Part IX. This includes re-proving and generalizing the adelic characterization of genus 0 quantum K-theory found in [Givental A., Tonita V., in Symplectic, Poisson, and Noncommutative Geometry, Math. Sci. Res. Inst. Publ., Vol. 62, Cambridge University Press, New York, 2014, 43-91]. Extending some results of Part VIII, we derive the invariance of a certain variety (the ''big J-function''), constructed from the genus 0 descendant potential of permutation-equivariant quantum K-theory, under the action of certain finite difference operators in Novikov's variables, apply this to reconstructing the whole variety from one point on it, and give an explicit description of it in the case of the point target space.
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| first_indexed | 2025-12-17T12:04:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210719 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:35Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
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| spelling | Givental, Alexander 2025-12-15T15:32:23Z 2020 Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0. Alexander Givental. SIGMA 16 (2020), 031, 16 pages 1815-0659 2020 Mathematics Subject Classification: 14N35 arXiv:1710.02376 https://nasplib.isofts.kiev.ua/handle/123456789/210719 DOI: https://doi.org/10.3842/SIGMA.2020.031 We extract genus 0 consequences of the all genera quantum HRR formula proved in Part IX. This includes re-proving and generalizing the adelic characterization of genus 0 quantum K-theory found in [Givental A., Tonita V., in Symplectic, Poisson, and Noncommutative Geometry, Math. Sci. Res. Inst. Publ., Vol. 62, Cambridge University Press, New York, 2014, 43-91]. Extending some results of Part VIII, we derive the invariance of a certain variety (the ''big J-function''), constructed from the genus 0 descendant potential of permutation-equivariant quantum K-theory, under the action of certain finite difference operators in Novikov's variables, apply this to reconstructing the whole variety from one point on it, and give an explicit description of it in the case of the point target space. This material is based upon work supported by the National Science Foundation under Grant DMS-1611839, by the IBS Center for Geometry and Physics, POSTECH, Korea, and by IHES, France. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 Article published earlier |
| spellingShingle | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 Givental, Alexander |
| title | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 |
| title_full | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 |
| title_fullStr | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 |
| title_full_unstemmed | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 |
| title_short | Permutation-Equivariant Quantum K-Theory X. Quantum Hirzebruch-Riemann-Roch in Genus 0 |
| title_sort | permutation-equivariant quantum k-theory x. quantum hirzebruch-riemann-roch in genus 0 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210719 |
| work_keys_str_mv | AT giventalalexander permutationequivariantquantumktheoryxquantumhirzebruchriemannrochingenus0 |