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2016 Gromov–Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda hierarchies
Todor Milanov, Yefeng Shen, Hsian-Hua Tseng
Geom. Topol. 20(4): 2135-2218 (2016). DOI: 10.2140/gt.2016.20.2135

Abstract

We construct an integrable hierarchy in the form of Hirota quadratic equations (HQEs) that governs the Gromov–Witten invariants of the Fano orbifold projective curve a1,a2,a31. The vertex operators in our construction are given in terms of the K–theory of a1,a2,a31 via Iritani’s Γ–class modification of the Chern character map. We also identify our HQEs with an appropriate Kac–Wakimoto hierarchy of ADE type. In particular, we obtain a generalization of the famous Toda conjecture about the GW invariants of 1 to all Fano orbifold curves.

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Todor Milanov. Yefeng Shen. Hsian-Hua Tseng. "Gromov–Witten theory of Fano orbifold curves, Gamma integral structures and ADE-Toda hierarchies." Geom. Topol. 20 (4) 2135 - 2218, 2016. https://doi.org/10.2140/gt.2016.20.2135

Information

Received: 12 December 2014; Accepted: 5 November 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06628602
MathSciNet: MR3548465
Digital Object Identifier: 10.2140/gt.2016.20.2135

Subjects:
Primary: 14N35 , 17B69

Keywords: ADE-Toda hierarchies , Fano orbifold curves , Gromov–Witten theory

Rights: Copyright © 2016 Mathematical Sciences Publishers

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