2016/10/25 by Raimundas Vidūnas, Yang‐Hui He, Vidunas, Raimundas +1 · 3 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Algebraic Geometry and Number Theory #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1610.08075
Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering maps from elliptic curves to the Riemann sphere with simpler (univariate) genus zero Belyi maps, as well as by (2) composing further with isogenies between elliptic curves. This gives many new explicit dessins on the doubly periodic plane, including several which have been realized in the physics literature as so-called brane-tilings in the context of quiver gauge theories.