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Mathematics > Algebraic Geometry

arXiv:2210.08939 (math)
[Submitted on 17 Oct 2022]

Title:Blow-ups and the quantum spectrum of surfaces

Authors: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.
Comments: 24 pages. Comments are welcome
Subjects: Algebraic Geometry (math.AG)
MSC classes: Primary 14N35, Secondary 53D45, 14E05
Cite as: arXiv:2210.08939 [math.AG]
  (or arXiv:2210.08939v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2210.08939

Submission history

From: Ádám Gyenge [view email]
[v1] Mon, 17 Oct 2022 11:04:52 UTC (26 KB)
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