|Date: Wednesday, April 22, 2015
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: Log discrepancy of Isolated singularities and Reeb orbits.
Abstract: 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 to 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 of Mumford in dimension 2.
Speaker: Mark Mclean
Institution: Stony Brook University