2017/11/10 by Jürgen Bokowski, Michael Cuntz · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Finite Group Theory Research #Genus #Quartic function #Riemann surface #Surface (topology) #Realization (probability) #Combinatorics #Mathematics #Pure mathematics #Geometry #Statistics #Biology #Zoology
paper · pdf · doi:10.26493/2590-9770.1186.258
openalex publication_date 2017/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A Hurwitz surface, named after Adolf Hurwitz, is a compact Riemann surface with precisely 84(g − 1) automorphisms, where g is the genus of the surface. The Hurwitz surface of least genus is the Klein quartic of genus 3. A polyhedral realization without self-intersections of Klein’s quartic of genus 3 was found by E. Schulte and J. M. Wills in 1985. For the next possible genus of a Hurwitz surface, i.e., for the genus 7 case with 72 vertices, we provide a polyhedral realization without self-intersections. We also show a topological representation for which we have a corresponding model.