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Minimal surfaces of general type with \(p_g = q = 0\) arising from Shimura surfaces. (English) Zbl 1401.14183
Summary: 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.

14J50 Automorphisms of surfaces and higher-dimensional varieties
14G35 Modular and Shimura varieties
14J29 Surfaces of general type
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