AbstractsMathematics

Tautological Bundles on the Hilbert Scheme of Points and the Normality of Secant Varieties.

by Brooke Susanna Ullery




Institution: University of Michigan
Department: Mathematics
Degree: PhD
Year: 2015
Keywords: secant varieties; Mathematics; Science
Record ID: 2061367
Full text PDF: http://hdl.handle.net/2027.42/111531


Abstract

In this dissertation, we study the geometry of secant varieties and their connections to certain tautological bundles on Hilbert schemes of points. Our main theorem shows that the first secant variety of a projective variety embedded by a sufficiently positive line bundle is a normal variety. As an application, we deduce the the secant variety of a general canonical curve of genus at least seven is normal. We also give conjectures toward the normality of higher secant varieties of curves.