Vol. 76, No. 1, 1978

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A class of algebraic surfaces of general type constructed from quaternion algebras

Ira H. Shavel

Vol. 76 (1978), No. 1, 221–245

This paper is concerned with a class of algebraic surfaces of general type constructed from indefinite division quaternion algebras whose centers are totally real number fields. These surfaces are quotients of the product of two upper half planes by Fuchsian groups obtained from the unit groups of maximal orders of such algebras. In the case where the field is real quadratic, we give smoothness conditions for the resulting surfaces and list all smooth surfaces of geometric genus 0. Finally, we give a lower bound for the torsion part of H2(Z).

Mathematical Subject Classification 2000
Primary: 14J20
Secondary: 14J25, 10D20, 10D05
Received: 26 July 1977
Published: 1 May 1978
Ira H. Shavel