Speaker: Mingmin Shen (Cambridge)

Title: Rational curves on Fano threefolds of Picard number one.

Abstract: It is well known that Fano varieties are rationally connected. In this talk I will explain how the Picard number puts restriction on the geometry of rational curves on a Fano threefold from a deformation point of view. To be more precise, we call a rational curve balanced if the normal bundle splits into a direct sum of line bundles whose degrees are distributed as evenly as possible. Then we show that a general rational curve on a Fano threefold is balanced with the only exception being a conic on P^3.