FUNDAMENTAL GROUPS OF GALOIS CLOSURES OF GENERIC PROJECTIONS

摘要

For the Galois closure X-gal of a generic projection from a surface X, it is believed that pi(1) (X-gal) gives rise to new invariants of X. However, in all examples this group is surprisingly simple. In this article, we offer all explanation for this phenomenon: We compute a quotient of pi(1) (X-gal) that depends on pi(1)(X) and data from the generic projection only. In all known examples, this quotient is in fact isomorphic to pi(1) (X-gal). As a by product, we simplify the computations of Moishezon, Teicher and others.