Nonexistence of unbalanced rational curves on Fano threefolds -- Mingmin Shen, February 5, 2010

A rational curve on a variety is called "unbalanced" if its normal bundle does not split evenly. We will explore how the existence of lots of unbalanced rational curves affects the structure of the variety. In particular, we show that there is no unbalanced components of very free rational curves on prime Fano threefolds.