A construction of smooth varieties admitting small contractions

TL;DR

This paper presents a method to construct smooth varieties with small contractions from any smooth projective variety, generalizing previous examples and providing conditions for nef divisors, leading to new weak Fano fourfolds.

Contribution

It introduces a new construction technique for smooth varieties with small contractions and extends Kawamata's four-dimensional example to a broader class.

Findings

Constructed smooth varieties with small contractions from arbitrary smooth projective varieties.

Provided conditions under which divisors on these varieties are nef.

Produced new weak Fano fourfolds from products of del Pezzo surfaces.

Abstract

We construct smooth varieties admitting small contractions from arbitrary smooth projective varieties. This construction generalizes Kawamata's four-dimensional example. We also give sufficient conditions for divisors on these varieties to be nef. As an application, we obtain weak Fano fourfolds from products of two del Pezzo surfaces.