|Institution:||University of Michigan|
|Keywords:||secant varieties; Mathematics; Science|
|Full text PDF:||http://hdl.handle.net/2027.42/111531|
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.