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arXiv · 2210.08939

Blow-ups and the quantum spectrum of surfaces

Ádám Gyenge·Szilárd Szabó
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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.

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Ádám Gyenge, Szilárd Szabó. 2022-10-17. Blow-ups and the quantum spectrum of surfaces. https://arxiv.org/abs/2210.08939

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