Partially ample subvarieties of projective varieties

TL;DR

This paper introduces partially ample subvarieties in projective varieties, extending previous concepts, and demonstrates their widespread presence along with applications to connectedness properties of morphism pre-images.

Contribution

It generalizes Ottem's ample subvarieties to a broader class called partially ample subvarieties and explores their properties and implications.

Findings

Partially ample subvarieties are common in projective varieties.

A connectedness theorem for pre-images under morphisms is established.

The work extends the theory of ample subvarieties to a more general setting.

Abstract

We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms, reminiscent to a problem posed by Fulton-Hansen.