Comments on the links between su(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards

1996/04/18 by M. Bauer, Michel Bauer, A. Coste +4 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1016/s0393-0440(96)00027-7

published as J.Geom.Phys. 22 (1997) 134-189 · 56 pages, 4 eps figures, LaTeX, uses epsf

arxiv created 1996/04/18 · openalex publication_date 1997/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.

Citations

• Implications of an arithmetical symmetry of the commutant for modular invariants

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