Smooth Fano varieties with pseudoindex equal to half of their dimension

TL;DR

This paper classifies smooth Fano varieties with a specific pseudoindex condition, focusing on those admitting a birational contraction of an extremal ray, providing new insights into their structure.

Contribution

It offers a classification of complex smooth Fano varieties with pseudoindex equal to half their dimension that admit a birational extremal contraction.

Findings

Classification of such Fano varieties achieved

Characterization of their geometric structure provided

New connections between pseudoindex and birational contractions established

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 $\frac{\dim X}{2}$.