(1) Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany
Abstract:
In this paper we generalise F. Cataneses work on singular (/2)2-covers to arbitrary finite abelian covers of algebraic surfaces. We determine the contribution of singularities to the invariants , K2, q, pg, Pn and the canonical sheaf. We use these computations to construct a surface of general type with birational canonical map 1, pg=4 and K2=31. Mathematics Subject Classification (2000):14J29, 14J17, 14J25, 14E20
s work on singular (
/2
, K 2, q, p g , P n and the canonical sheaf. We use these computations to construct a surface of general type with birational canonical map 
1, p g =4 and K 2 =31. Mathematics Subject Classification (2000):
14J29, 14J17, 14J25, 14E20