|
|||||
|
|
|
|
|
|
|
|
|
Gromov–Witten theory of
Fano orbifold curves, Gamma integral structures and ADE-Toda
hierarchies
Todor Milanov, Yefeng Shen and Hsian-Hua Tseng |
|
Geometry & Topology 20 (2016) 2135–2218
|
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 . The vertex operators in our construction are given in terms of the –theory of via Iritani’s –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 to all Fano orbifold curves. |
Keywords
Gromov–Witten theory, Fano orbifold curves, ADE-Toda
hierarchies
|
Mathematical Subject Classification 2010
Primary: 14N35, 17B69
|
References |
Publication
Received: 12 December 2014
Accepted: 5 November 2015
Published: 15 September 2016
Proposed: Yasha Eliashberg
Seconded: Gang Tian, Jim Bryan
|
Authors |
| Todor Milanov | |
| Kavli IPMU University of Tokyo (WPI) 5-1-5 Kashiwanoha Kashiwa 2778583 Japan |
|
| Yefeng Shen | |
| Department of Mathematics Stanford University 450 Serra Mall, Building 380 Stanford, CA 94305 United States |
|
| Hsian-Hua Tseng | |
| Department of Mathematics Ohio State University 100 Math Tower 231 West 18th Avenue Columbus, OH 43210 United States |
|
|
