Group representations on Riemann-Roch spaces of some Hurwitz curves

2006/11/17 by David Joyner, Joyner, David, Amy Ksir +3
Mathematics · #14C20 #14F25 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14C20 #msc:14F25

paper · pdf · doi:10.48550/arxiv.math/0611547

26 pages

arxiv created 2006/11/17 · openalex publication_date 2006/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q>1 denote an integer relatively prime to 2,3,7 and for which G=PSL(2,q) is a Hurwitz group for a smooth projective curve X defined over C. We compute the G-module structure of the Riemann-Roch space L(D), where D is an invariant divisor on X of positive degree. This depends on a computation of the ramification module, which we give explicitly. In particular, we obtain the decomposition of H¹(X,C) as a G-module.

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