On Fano manifolds with a birational contraction sending a divisor to a curve

TL;DR

This paper investigates smooth Fano varieties of dimension at least 4 with a specific type of birational contraction, establishing an upper bound of 5 on their Picard number.

Contribution

It proves that such Fano varieties with a divisor contracted to a curve have Picard number at most 5, providing a new restriction on their structure.

Findings

Picard number of X is ≤ 5 under the given contraction

Characterization of Fano varieties with a divisor contracted to a curve

Constraints on the geometry of Fano varieties with specific contractions

Abstract

Let X be a smooth Fano variety of dimension at least 4. We show that if X has an elementary birational contraction sending a divisor to a curve, then the Picard number of X is smaller or equal to 5.