Liouville Equation And Schottky Problem
High Energy Physics - Theory
2009-10-22 v2 alg-geom
Algebraic Geometry
Abstract
An Ansatz for the Poincar\'e metric on compact Riemann surfaces is proposed. This implies that the Liouville equation reduces to an equation resembling a non chiral analogous of the higher genus relationships (KP equation) arising in the framework of Schottky's problem solution. This approach connects uniformization (Fuchsian groups) and moduli space theories with KP hierarchy. Besides its mathematical interest, the Ansatz has some applications in the framework of quantum Riemann surfaces arising in 2D gravity.
Keywords
Cite
@article{arxiv.hep-th/9310066,
title = {Liouville Equation And Schottky Problem},
author = {Marco Matone},
journal= {arXiv preprint arXiv:hep-th/9310066},
year = {2009}
}
Comments
12 pages, LaTex file. Expanded version and misprints corrected