Eduard Looijenga

Topological Stability of Smooth Mappings

Construction of canonical stratifications.- Stratifications and flows.- Unfoldings of smooth map-germs.- Proof of the topological stability theorem.

On the tautological ring of Mg

We prove that any product of tautological classes of ℳg of degreed (in the Chow ring of ℳg with rational coefficients) vanishes ford>g−2 and is proportional to the class of the hyperelliptic locus in degreeg−2.

A Lie algebra attached to a projective variety

A bstract . Each choice of a Kähler class on a compact complex manifold defines an action of the Lie algebra sl(2) on its total complex cohomology. If a nonempty set of such Kähler classes is given, then we prove that the corresponding sl(2)-copies generate a semisimple Lie algebra. We investigate the formal properties of the resulting representation and we work things out explicitly in the case of complex tori, hyperkähler manifolds and flag varieties. We pay special attention to the cases where this leads to a Jordan algebra structure or a graded Frobenius algebra.

Cellular Decompositions of Compactified Moduli Spaces of Pointed Curves

To a closed connected oriented surface S of genus g and a nonempty finite subset P of S is associated a simplicial complex (the arc complex) that plays a basic role in understanding the mapping class group of the pair (S, P). It is known that this arc complex contains in a natural way the product of the Teichmuller space of (S, P) with an open simplex. In this paper we give an interpretation for the whole arc complex and prove that it is a quotient of a Deligne-Mumford extension of this Teichmuller space and a closed simplex. We also describe a modification of the arc complex in the spirit of Deligne-Mumford.

Prym representations of mappings class groups

AbstractLet S be a closed orientable surface of genus at least 2 and let

Uniformization by Lauricella Functions — An Overview of the Theory of Deligne-Mostow

\widetilde S

Compactifications defined by arrangements I: The Ball Quotient case

to S be a connected finite abelian covering with covering group

Milnor number and Tjurina number of complete intersections

G