2013/08/20 by Matthew Stover, Stover, Matthew · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.AG #math.GT
paper · pdf · doi:10.48550/arxiv.1308.4353
Several improvements incorporating referee's comments. To appear in Math. Z
openalex publication_date 2013/08/20 · arxiv created 2014/02/19 · arxiv updated 2014/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the analogue of Hurwitz curves, smooth projective curves C of genus g ≥ 2 that realize equality in the Hurwitz bound |Aut(C)| ≤ 84 (g - 1), to smooth compact quotients S of the unit ball in ℂ2. When S is arithmetic, we show that |Aut(S)| ≤ 288 e(S), where e(S) is the (topological) Euler characteristic, and in the case of equality show that S is a regular cover of a particular Deligne--Mostow orbifold. We conjecture that this inequality holds independent of arithmeticity, and note that work of Xiao makes progress on this conjecture and implies the best-known lower bound for the volume of a complex hyperbolic 2-orbifold.