Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs

2020/05/28 by Tim Graefnitz, Graefnitz, Tim · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2005.14018

openalex publication_date 2020/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a log Calabi-Yau pair (X,D) consisting of a smooth del Pezzo surface X of degree ≥ 3 and a smooth anticanonical divisor D. We prove a correspondence between genus zero logarithmic Gromov-Witten invariants of X intersecting D in a single point with maximal tangency and the consistent wall structure appearing in the dual intersection complex of (X,D) from the Gross-Siebert reconstruction algorithm. More precisely, the logarithm of the product of functions attached to unbounded walls in the consistent wall structure gives a generating function for these invariants.

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