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A Quadratically Enriched Correspondence Theorem

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arxiv 2309.11706 v2 pith:JYWVECE3 submitted 2023-09-21 math.AG math.AT

Andrés Jaramillo Puentes , Sabrina Pauli This is my paper · ORCID
classification math.AGmath.AT
keywords correspondencecurvescountedenrichmentmikhalkinquadraticquadraticallytheorem
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We quadratically enrich Mikhalkin's correspondence theorem. That is, we prove a correspondence between algebraic curves on a toric surface counted with Levine's quadratic enrichment of the Welschinger sign, and tropical curves counted with a quadratic enrichment of Mikhalkin's multiplicity for tropical curves.

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  1. Quadratically Enriched Plane Curve Counting via Tropical Geometry

    math.AG 2025-02 conditional novelty 7.0 of 10

    A correspondence theorem equates quadratically enriched algebraic curve counts with conjugate point conditions to tropical counts with double point conditions, and a floor diagram algorithm computes them.

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