A graphical interface for the Gromov--Witten theory of curves
Abstract
We explore the explicit relationship between the descendant Gromov--Witten theory of target curves, operators on Fock spaces, and tropical curve counting. We prove a classical/tropical correspondence theorem for descendant invariants and give an algorithm that establishes a tropical Gromov--Witten/Hurwitz equivalence. Tropical curve counting is related to an algebra of operators on the Fock space by means of bosonification. In this manner, tropical geometry provides a convenient "graphical user interface" for Okounkov and Pandharipande's celebrated GW/H correspondence. An important goal of this paper is to spell out the connections between these various perspectives for target dimension 1, as a first step in studying the analogous relationship between logarithmic descendant theory, tropical curve counting, and Fock space formalisms in higher dimensions.
Keywords
Cite
@article{arxiv.1604.07250,
title = {A graphical interface for the Gromov--Witten theory of curves},
author = {Renzo Cavalieri and Paul Johnson and Hannah Markwig and Dhruv Ranganathan},
journal= {arXiv preprint arXiv:1604.07250},
year = {2018}
}
Comments
26 pages, 7 figures. v2: Minor expository changes. Final version to appear in the Proceedings of the AMS Algebraic Geometry Summer Institute (Salt Lake City, 2015)