Harmonic bundles and Toda lattices with opposite sign
Differential Geometry
2015-06-12 v1 Mathematical Physics
Algebraic Geometry
Classical Analysis and ODEs
math.MP
Abstract
We study a certain type of wild harmonic bundles in relation with a Toda equation. We explain how to obtain a classification of the real valued solutions of the Toda equation in terms of their parabolic weights, from the viewpoint of the Kobayashi-Hitchin correspondence. Then, we study the associated integrable variation of twistor structure. In particular, we give a criterion for the existence of an integral structure. It follows from two results. One is the explicit computation of the Stokes factors of a certain meromorphic flat bundle. The other is an explicit description of the associated meromorphic flat bundle. We use the opposite filtration of the limit mixed twistor structure with an induced torus action.
Keywords
Cite
@article{arxiv.1301.1718,
title = {Harmonic bundles and Toda lattices with opposite sign},
author = {Takuro Mochizuki},
journal= {arXiv preprint arXiv:1301.1718},
year = {2015}
}