Blow-ups and the quantum spectrum of surfaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909673512239104 |
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| author | Gyenge, Ádám Szabó, Szilárd |
| author_facet | Gyenge, Ádám Szabó, Szilárd |
| contents | We investigate the behaviour of the spectrum of the quantum (or Dubrovin) connection of smooth projective surfaces under blow-ups. Our main result is that for small values of the parameters, the quantum spectrum of such a surface is asymptotically the union of the quantum spectrum of a minimal model of the surface and a finite number of additional points located "close to infinity", that correspond bijectively to the exceptional divisors. This proves a conjecture of Kontsevich in the surface case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08939 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Blow-ups and the quantum spectrum of surfaces Gyenge, Ádám Szabó, Szilárd Algebraic Geometry Primary 14N35, Secondary 53D45, 14E05 We investigate the behaviour of the spectrum of the quantum (or Dubrovin) connection of smooth projective surfaces under blow-ups. Our main result is that for small values of the parameters, the quantum spectrum of such a surface is asymptotically the union of the quantum spectrum of a minimal model of the surface and a finite number of additional points located "close to infinity", that correspond bijectively to the exceptional divisors. This proves a conjecture of Kontsevich in the surface case. |
| title | Blow-ups and the quantum spectrum of surfaces |
| topic | Algebraic Geometry Primary 14N35, Secondary 53D45, 14E05 |
| url | https://arxiv.org/abs/2210.08939 |