A quadratically enriched correspondence theorem

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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Publication Details

Journal
Journal of the European Mathematical Society
Published
2025-09-15
DOI
https://doi.org/10.4171/jems/1694
Primary Topic
Advanced Topics in Algebra
Type
article
Field-Weighted Citation Impact
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article

A quadratically enriched correspondence theorem

Andrés Jaramillo Puentes, Sabrina Pauli
Journal of the European Mathematical Society
Advanced Topics in Algebra
article

A quadratically enriched correspondence theorem

Andrés Jaramillo Puentes, Sabrina Pauli
article en

Abstract

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.

Journal of the European Mathematical Society
Technische Universität Darmstadt (DE), University of Tübingen (DE)
Openalex Percentile: Top 68%
Advanced Topics in Algebra
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A quadratically enriched correspondence theorem — Andrés Jaramillo Puentes, Sabrina Pauli · Journal of the European Mathematical Society (2025) | TGRS Research Map | TGRS