Werner Kleinert of Humboldt University at Berlin will speak on "The Irreducible Components of the Singular Locus in Moduli Spaces of Curves."

Abstract
We consider the moduli space M(g)  of non-singular projective algebraic curves of genus  g > 2 over an algebraically closed field k of arbitrary characteristic and,in particular, the classical special case of the moduli space of compact Riemann surfaces of genus  g . The moduli space M(g)  is a quasi-projective variety of dimension  3g-3 , with fairly mild singularities, and the singular locus  B(g) in  M(g) is basically the locus of isomorphism classes of curves with non-trivial automorphisms.  The aim of my talk is to describe an explicit,purely algebraic construction of the irreducible components of the singular locus  B(g), which works in any characteristic, and to give a geometric characterization of these irreducible components in terms of automorphisms and coverings of algebraic curves.  At the end, and as an application of this general approach, the 0-dimensional irreducible components (i.e.,the isolated singularities in  M(g) ) will be completely characterized and counted.  The general algebraic approach presented here exhibits an interesting contrast to the classical methods in the moduli theory of Riemann surfaces (such as uniformization, Fuchsian groups, Teichmuller theory,etc.).

Tuesday, September 28, 4:30 p.m. in Krieger 300
Refreshments will be served in Krieger 211 at 3:30 p.m.