Blow-ups and the quantum spectrum of surfaces
Algebraic Geometry
2025-07-04 v3
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.
Keywords
Cite
@article{arxiv.2210.08939,
title = {Blow-ups and the quantum spectrum of surfaces},
author = {Ádám Gyenge and Szilárd Szabó},
journal= {arXiv preprint arXiv:2210.08939},
year = {2025}
}
Comments
Final version. To appear in Advances in Mathematics