On Eckl's pseudo-effective reduction map

Abstract

Suppose that X is a complex projective variety and L is a pseudo-effective divisor. A numerical reduction map is a quotient of X by all subvarieties along which L is numerically trivial. We construct two variants: the L-trivial reduction map and the pseudo-effective reduction map of [Eckl05]. We show that these maps capture interesting geometric properties of L and use them to analyze abundant divisors.

26 pages, v3: small revisions in introduction

References in corpus (2)

• Varieties with generically nef tangent bundles
• Numerical trivial foliations, Iitaka Fibrations and the numerical dimension

Cited by in corpus (2)

• Reduction maps and minimal model theory
• Asymptotic base loci on singular varieties