MEROMORPHIC FUNCTIONS ON THE LINE

                         V.Goryunov (Liverpool)

                              ABSTRACT

In 1891 Hurwitz made a conjecture yielding the number of topological
types of meromorphic functions on the complex line with fixed orders of
poles and fixed critical values assuming the functions Morse on the
complement to the poles.  Recently there appeared two combinatorial
proofs of the conjecture by Goulden and Jackson, and Strehl (both with
lots of very long and mysterious calculations).  We give an independent
proof, from the point of view of singularity theory.  The new proof is based
on the study of geometry of the moduli space of ordered tuples of points
on the line.