Title: Normal bundles of curves
Abstract: The normal bundles of a curve in an algebraic variety determine both how the curve can deform within the variety and more intrinsic geometric facts about the variety. For instance, if a variety contains a rational curve with ample normal bundle, it is separably rationally connected and satisfies several nice geometric properties. In this talk I will discuss two projects related to the study of normal bundles of curves in a variety, both joint with Izzet Coskun. First, I will present some examples of SRC varieties that can be found by explicitly looking at the ampleness of normal bundles of some rational curves. Second, I will present ongoing work studying the circumstances under which a curve in projective space has ample normal bundle.
