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Topological recursion for irregular spectral curves

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arxiv 1412.8334 v1 pith:D5Z2ZBXJ submitted 2014-12-29 math.GT math-phmath.COmath.MP

classification math.GTmath-phmath.COmath.MP
keywords spectralcurverecursionirregulartopologicalcurvesdessinsenfant
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abstract

We study topological recursion on the irregular spectral curve $xy^2-xy+1=0$, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve $xy^2=1$, which takes the place of the Airy curve $x=y^2$ to describe asymptotic behaviour of enumerative problems associated to irregular spectral curves. In particular, we calculate all one-point invariants of the spectral curve $xy^2=1$ via a new three-term recursion for the number of dessins d'enfant with one face.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Universal Correlators on Exponentially Ramified Spectral Curves

    math-ph 2026-07 conditional novelty 6.0 of 10

    Generalized topological recursion extends to spectral curves with essential singularities by replacing residues at the essential point with residues at ordinary meromorphic points.

  2. Quantum Curves in the Context of Symplectic Duality

    math-ph 2025-04 conditional novelty 6.0 of 10

    Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.

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