The Classification of Surfaces with pg = q = 0 Isogenous to a Product of Curves

I. C. Bauer, F. Catanese, F. Grunewald
2008 Pure and Applied Mathematics Quarterly  
We classify all the surfaces with p g = q = 0 which admit an unramified covering isomorphic to a product of curves. Beyond the trivial case P 1 × P 1 we find 17 families which we explicitly describe. We reduce the problem to a combinatorial description of certain generating systems for finite groups which we solve using also MAGMA's library of groups of small order.
doi:10.4310/pamq.2008.v4.n2.a10 fatcat:75gymd2p45g7lamvhs5fib3ve4