Skip to Main Content
Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Tropical correspondence for smooth del Pezzo log Calabi-Yau pairs

Author: Tim Graefnitz
Journal: J. Algebraic Geom. 31 (2022), 687-749
Published electronically: June 24, 2022
Full-text PDF

Abstract | References | Additional Information

Abstract: Consider a log Calabi-Yau pair $(X,D)$ consisting of a smooth del Pezzo surface $X$ of degree $\geq 3$ 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.

References [Enhancements On Off] (What's this?)


Additional Information

Tim Graefnitz
Affiliation: Department of Mathematics, University of Hamburg, Germany

Received by editor(s): October 6, 2020
Received by editor(s) in revised form: September 8, 2021, October 15, 2021, and March 10, 2022
Published electronically: June 24, 2022
Additional Notes: This work was supported by the DFG funded Research Training Group 1670 “Mathematics Inspired by String theory and Quantum Field Theory”
Article copyright: © Copyright 2022 University Press, Inc.