Jet bundle and Infinitesimal Neighborhoods I
Speaker: Shilin Yu, Penn State University
Abstract: A classical theorem in differential topology says that any submanifold of a smooth manifold admits a turbular neighborhood which is diffeomorphic to the total space of its normal bundle. In the complex analytic world, this is not even close to being true if the word 'diffeomorphism' is substituted by 'biholomorphism'. An alternative question one could consider is to compare the infinitesimal neighborhood of a complex submanifold with that of the zero section within its normal bundle. I will discuss the special yet important case of the diagonal embedding of a complex manifold X into X x X, which is related to the notion of jet bundle (of holomorphic functions). I will state and, if time permits, sketch the proof of a classical result on the diagonal embedding by Kapranov in the Kahler case.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm