Some remarks on cones of partially ample divisors

TL;DR

This paper investigates the structure of cones of q-ample divisors on smooth complex varieties, revealing conditions under which their boundaries coincide with those of nef cones, especially in Fano cases.

Contribution

It identifies specific regions where the closure of q-ample cones and nef cones share the same boundary in certain varieties, advancing understanding of their geometric relationship.

Findings

In certain cases, the q-ample cone boundary coincides with the nef cone boundary.

The results are particularly relevant for Fano and almost Fano varieties.

Provides new insights into the geometry of divisor cones on complex varieties.

Abstract

We study the cones of q-ample divisors on smooth complex varieties. In favourable cases, we identify a part where the closure of this cone and the nef cone have the same boundary. This is especially interesting for Fano (or almost Fano) varieties.