We provide simpler proofs of several boundedness theorems, contained in in articles [2], [3], for log surfaces of general type with semi log canonical singularities. At the same time, we make these proofs e ective, with explicit upper bounds.

The moduli space M of surfaces of general type with pg = q = 1, K 2 = g = 3 (where g is the genus of the Albanese fibration) was constructed by Catanese and Ciliberto in [CaCi93]. In this paper we characterize the subvariety M 2 ⊂ M corresponding to surfaces containing a genus 2 pencil, and moreover we show that there exists a non-empty, dense subset M 0 ⊂ M which parametrizes isomorphism class...

We generalise a method of Xiao Gang to construct ’prototypes’ of fibred surfaces with maximal irregularity without being a product. This enables us, in the case of fibre genus g = 3 to describe the possible singular fibres and to calculate the invariants of these surfaces. We also prove structure theorems on the moduli space for fibred surfaces with fibre genus g = 2 and g = 3. Mathematics Subj...

This theorem has a number of geometric and number theoretic consequences that will be discussed in the final section of this paper. In particular, assuming Lang’s conjecture on rational points of varieties of general type, we can prove a uniform bound on the number of rational points on a surface of general type not contained in rational or elliptic curves. This theorem is a special case of the...