Asian Journal of Mathematics

Volume 21 (2017)

Number 4

Minimal surfaces of general type with $p_g = q = 0$ arising from Shimura surfaces

Pages: 775 – 790

DOI: https://dx.doi.org/10.4310/AJM.2017.v21.n4.a6

Authors

Amir Džambić (Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Germany)

Xavier Roulleau (Laboratoire de Mathématiques et Applications, Université de Poitiers, Futuroscope Chasseneuil, France)

Abstract

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.

Keywords

Shimura surfaces, surface automorphisms, quotients by finite groups, surfaces of general type

2010 Mathematics Subject Classification

14G35, 14J29, 14J50

Full Text (PDF format)

Received 3 September 2015

Published 25 August 2017