Partially ample subvarieties of projective varieties
Mihai Halic

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.
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