Given a smooth complex surface , and a compact connected global normal crossings divisor , we consider the local fundamental group , where is a good tubular neighbourhood of . One has an exact sequence , and the kernel is normally generated by geometric loops around the curve . Among the main results, which are strong generalizations of a well known theorem of Mumford, is the nontriviality of in , provided all the curves of genus zero have selfintersection (in particular this holds if the canonical divisor is nef on ), and under the technical assumption that the dual graph of is a tree.
Cite this article
Fabrizio Catanese, Surface classification and local and global fundamentals groups, I. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 2, pp. 135–153DOI 10.4171/RLM/459