Almost duality for Saito structure and complex reflection groups
Algebraic Geometry
2018-02-07 v2
Abstract
We reformulate Dubrovin's almost duality of Frobenius structures to Saito structures without metric. Then we formulate and study the existence and uniqueness problem of the natural Saito structure on the orbit spaces of finite complex reflection groups from the viewpoint of the almost duality. We give a complete answer to the problem for the irreducible groups.
Keywords
Cite
@article{arxiv.1612.03643,
title = {Almost duality for Saito structure and complex reflection groups},
author = {Yukiko Konishi and Satoshi Minabe and Yuuki Shiraishi},
journal= {arXiv preprint arXiv:1612.03643},
year = {2018}
}
Comments
v2: 50 pages, version to appear in Journal of Integrable Systems. Corrected Proposition 2.9 and Lemma 6.6 (= Lemma 6.5 in v1) following the referee's suggestion. Expanded sections 4.2 and 7.3 on the relationship with the works of Arsie-Lorenzoni and Kato-Mano-Sekiguchi. Other minor changes