Algebraic bounds on analytic multiplier ideals

Details Algebraic bounds on analytic multiplier ideals Algebraic bounds on analytic multiplier ideals

2011-09-21

arxiv.org/abs/1109.4452v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

We show that the multiplier ideal of the metric of minimal singularities on a pseudo-effective line bundle L is contained in the asymptotic multiplier ideal of L increased by a small ample divisor. Often the former ideal is contained in the diminished ideal, a "continuous" extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. We characterize abundance using the diminished ideal, showing that in this case the geometric and analytic information coincide.

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