Smooth Fano varieties with pseudoindex equal to half of their dimension

Abstract

Let $X$ be a complex smooth Fano variety of dimension $n$. Assume that $X$ admits a birational contraction of an extremal ray. In this paper, we give a classification of such $X$ when the pseudoindex is equal to $\frac{\dim X}{2}$.

14 pages, to appear in the Journal of the Mathematical Society of Japan