Orateur
M.
Mark McLean
(Stony Brook)
Description
Let A be an affine variety inside a complex N dimensional vector space which has an isolated singularity at the origin. The intersection of A with a very small sphere turns out to be a manifold called the link of A. The link has a natural hyperplane distribution called a contact structure. If the singularity is numerically Q-Gorenstein then we can assign an invariant of our singularity called the minimal discrepancy. We relate the minimal discrepancy with the contact geometry of our link. As a result we show that if the link of A is contactomorphic to the link of C^3 and A is normal then A is smooth at 0. This generalizes a Theorem by Mumford in dimension 2.
