Seminar in Real & Complex Geometry

Tuesday, 19.03.2012, 15:00-16:30, Schreiber building, room 210

Dmitry Kerner, University of Toronto

Discriminant of transversal singularity type


Consider a projective (complex) variety X with non-isolated singular locus Z. The baby case is the Whitney umbrella: x^2z=y^2. At any smooth point of Z, take the transversal section of complementary dimension. Intersecting this section with X gives an isolated singularity. This transversal type is generically constant. At some points of Z it degenerates to higher singularities. "How many times" such a degeneration occurs? More precisely, the "discriminant of transversal type" is a scheme supported at these points. We define the relevant scheme structure and compute the cohomology class of this discriminant. Joint work with M. Kazarian and A. Nemethi.