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Conditions for the vanishing of the genus-2 G-function


Authors: Xiaobo Liu and Xin Wang
Journal: Trans. Amer. Math. Soc. 367 (2015), 8975-8996
MSC (2010): Primary 53D45; Secondary 14N35
DOI: https://doi.org/10.1090/S0002-9947-2015-06540-4
Published electronically: February 20, 2015
MathSciNet review: 3403077
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Abstract: In this paper we give some sufficient conditions for the vanishing of the genus-2 G-function, which was introduced by B. Dubrovin, S. Liu and Y. Zhang in 2012. As a corollary we prove their conjecture for the vanishing of the genus-2 G-function for ADE singularities.


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Xiaobo Liu
Affiliation: Beijing International Center for Mathematical Research, Beijing University, Beijing, People’s Republic of China – and – Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: xbliu@math.pku.edu.cn, xliu3@nd.edu

Xin Wang
Affiliation: School of Mathematical Sciences, Beijing University, Beijing, People’s Republic of China
Email: xinwang-1989@163.com

DOI: https://doi.org/10.1090/S0002-9947-2015-06540-4
Received by editor(s): December 5, 2013
Received by editor(s) in revised form: June 9, 2014
Published electronically: February 20, 2015
Additional Notes: The research of the first author was partially supported by NSF grant DMS-0905227, NSFC Tianyuan special fund 11226027, SRFDP grant 20120001110051, and Peking University 985 fund.
The research of the second author was partially supported by SRFDP grant 20120001110051.
Article copyright: © Copyright 2015 American Mathematical Society