Back to Algebraic Geometry Seminar: Fall 2014
Algebraic Geometry Seminar
Date: Tuesday, Dec 9, 2014
Time: 3:30PM - 4:30PM
Location: LCB 225
Mark McLean
Stony Brook University
Title |
Minimal Log Discrepancy of Isolated Singularities and Reeb Orbits. |
Abstract |
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 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. |
Algebraic Geometry