2001/11/08 by Kapil Hari Paranjape, Paranjape, Kapil Hari
Mathematics · #11G35 #14J20 #51A25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G35 #msc:14J20 #msc:51A25
paper · pdf · doi:10.48550/arxiv.math/0111091
8 Pages, AMSLaTeX
arxiv created 2002/04/08 · arxiv updated 2009/11/30
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterisation of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.