Consider a projective (complex) variety X with nonisolated 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.
