Back to Algebraic Geometry Seminar: Fall 2015
Algebraic Geometry Seminar
Date: Tuesday, Sep 15, 2015
Time: 3:30PM - 4:30PM
Location: JFB 102
Brooke Ullery
University of Utah
Title |
Normality of Secant Varieties |
Abstract |
If X is a smooth variety embedded in projective space, we can form a new variety by looking at the closure of the union of all the lines through 2 points on X. This is called the secant variety of X. Similarly, the Hilbert scheme of 2 points on X parametrizes all length 2 zero-dimensional subschemes. I will talk about how these two constructions are related. More specifically, I will show how we can use certain tautological vector bundles on the Hilbert scheme to help us understand the geometry of the secant variety, leading to a proof that for sufficiently positive embeddings of X, the secant variety is a normal variety. |
Algebraic Geometry