Positive cones of dual cycle classes

TL;DR

This paper explores generalized nef cones for higher codimension cycles on projective varieties, addressing issues in classical definitions and confirming expected properties of pseudoeffective cones across all dimensions.

Contribution

It introduces new generalizations of nef cones for higher codimension cycles that resolve classical pathologies and verifies their expected properties for pseudoeffective cones.

Findings

Generalized nef cones fix classical pathologies.

Confirmed properties of pseudoeffective cones for all k.

Provides a framework for higher codimension cycle analysis.

Abstract

We study generalizations for higher codimension cycles of several well-known definitions of the nef cone of divisors on a projective variety. These generalizations fix some of the pathologies exhibited by the classical nef cone of higher codimension classes. As an application, we recover the expected properties of the pseudoeffective cones $\overline{Eff}_{k}(X)$ for all k.