English

On Eckl's pseudo-effective reduction map

Algebraic Geometry 2011-09-22 v3

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.

Keywords

Cite

@article{arxiv.1103.1073,
  title  = {On Eckl's pseudo-effective reduction map},
  author = {Brian Lehmann},
  journal= {arXiv preprint arXiv:1103.1073},
  year   = {2011}
}

Comments

26 pages, v3: small revisions in introduction

R2 v1 2026-06-21T17:35:35.853Z