Gyenge, Ádám and Szabó, Szilárd (2025) Blow-ups and the quantum spectrum of surfaces. ADVANCES IN MATHEMATICS, 479. No.-110432. ISSN 0001-8708 (In Press)
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Official URL: https://doi.org/10.1016/j.aim.2025.110432
Abstract
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.
| Item Type: | Article |
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| Uncontrolled Keywords: | Quantum connection, Spectrum, Birational geometry, Surface, Newton polygon |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 29 Jul 2025 14:24 |
| Last Modified: | 29 Jul 2025 14:24 |
| URI: | https://real.mtak.hu/id/eprint/221620 |
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