2004/01/07 by Pascal Hubert, Hubert, Pascal, Samuel Lelièvre +1
Mathematics · #32G15 (37C35 37D50 30F30 14H55 30F35) #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals
paper · doi:10.48550/arxiv.math/0401056
openalex publication_date 2004/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that Teichmuller discs that pass through "integer points'' of the moduli space of abelian differentials are very special: they are closed complex geodesics. However, the structure of these special Teichmuller discs is mostly unexplored: their number, genus, area, cusps, etc. We prove that in genus two all translation surfaces in H(2) tiled by a prime number n > 3 of squares fall into exactly two Teichmuller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.