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 Ndimensional 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 QGorenstein, 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.
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Speaker: Mark Mclean
Institution: Stony Brook University
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