Algebraic Geometry Seminar
Atanas Atanasov
Citadel
Interpolation and vector bundles on curves
Abstract: We aim to address the following: When is there a (smooth) curve of degree $d$ and genus $g$ passing through $n$ general points in $\mathbb{P}^r$. Generalizations ask for the dimension of such curves, or replace the point incidence conditions with higher dimensional linear spaces. We will start by relating these statements to a property of the normal bundle of curves in projective space. Next, we will show how to address these questions for $r = 3$ and $d >= g + 3$. The demonstrated techniques generalize significantly and lead to an answer to our question for $d >= g + r$. This is joint work with E. Larson and D. Yang.
Wednesday February 10, 2016 at 4:00 PM in SEO 427