Eleonore Faber, University of Toronto
“Free and splayed divisors: singularities and transversality”
Free divisors are certain non-normal hypersurfaces in a complex manifold, whose singular loci have nice algebraic properties: the Jacobian ideals are Maximal Cohen Macaulay modules for the hypersurface rings. In this talk we give a short introduction to free divisors, also to their original definition (due to K. Saito) via logarithmic derivations and logarithmic differential forms. Using these logarithmic derivations we obtain a notion for transversality for singular hypersurfaces. The union of two such transversally intersecting hypersurface is then called a splayed divisor. We consider the relation of splayed divisors with free divisors and present several algebraic characterizations of them. This leads to a conjecture about the singularities of some well-known free divisors, namely, of normal crossing hypersurfaces.