Real-normalized differentials and the elliptic Calogero-Moser system

2011/08/21 by Samuel Grushevsky, Grushevsky, Samuel, I. M. Krichever +1 · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1108.4211

Abstract

In our recent works we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this paper we survey the relevant constructions and show how they are related to and motivated by the spectral theory of the elliptic Calogero-Moser integrable system.

Cited by

• Deformations of the Hill curves and isoperiodicity in the KdV and the sine-Gordon equations
• The r-matrix structure on the moduli space of framed Higgs pairs

Related

• Period realization of meromorphic differentials with prescribed invariants
• Principal stratum in the moduli space of real-normalized differentials with a single pole
• Real normalized differentials and Arbarello's conjecture
• Real-normalized differentials: limits on stable curves
• Connected components of the strata of the moduli space of meromorphic differentials