On Eckl's pseudo-effective reduction map

Details On Eckl's pseudo-effective reduction map On Eckl's pseudo-effective reduction map

2011-03-05

arxiv.org/abs/1103.1073v3

Mathematics

Algebraic Geometry

26 pages, v3: small revisions in introduction

Scientific paper

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.

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