Asian Journal of Mathematics
Volume 21 (2017)
Minimal surfaces of general type with $p_g = q = 0$ arising from Shimura surfaces
Pages: 775 – 790
Quaternionic Shimura surfaces are quotients of the product of two copies of the upper half plane by irreducible cocompact arithmetic groups. In the present paper we are interested in (smooth) quaternionic Shimura surfaces admitting an automorphism with one-dimensional fixed locus; such automorphisms are involutions. We propose a new construction of surfaces of general type with $q = p_g = 0$ as quotients of quaternionic Shimura surfaces by such involutions. These quotients have finite fundamental group.
Shimura surfaces, surface automorphisms, quotients by finite groups, surfaces of general type
2010 Mathematics Subject Classification
14G35, 14J29, 14J50
Paper received on 3 September 2015.