On Eckl’s pseudo-effective reduction map

Lehmann, Brian

doi:10.1090/S0002-9947-2013-05826-6

On Eckl’s pseudo-effective reduction map
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Trans. Amer. Math. Soc. 366 (2014), 1525-1549

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 Eckl (2005). We show that these maps capture interesting geometric properties of $L$ and use them to analyze abundant divisors.

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