A graphical interface for the Gromov-Witten theory of curves

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Date
2016-05-10MFO Scientific Program
Research in Pairs 2015Series
Oberwolfach Preprints;2016,06Author
Cavalieri, Renzo
Johnson, Paul
Markwig, Hannah
Ranganathan, Dhruv
Metadata
Show full item recordOWP-2016-06
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.