628 research outputs found
Algebraic bounds on analytic multiplier ideals
Given a pseudo-effective divisor L we construct the diminished ideal of L, a
"continuous" extension of the asymptotic multiplier ideal for big divisors to
the pseudo-effective boundary. For most pseudo-effective divisors L the
multiplier ideal of the metric of minimal singularities of L is contained in
the diminished ideal. We also characterize abundant divisors using the
diminished ideal, indicating that in this case the geometric and analytic
information should coincide.Comment: 27 pages; v3: corrected several mistake
On Eckl's pseudo-effective reduction map
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.Comment: 26 pages, v3: small revisions in introductio
Convexity and Zariski decomposition structure
This is the first part of our work on Zariski decomposition structures, where
we study Zariski decompositions using Legendre-Fenchel type transforms. In this
way we define a Zariski decomposition for curve classes. This decomposition
enables us to develop the theory of the volume function for curves defined by
the second named author, yielding some fundamental positivity results for curve
classes. For varieties with special structures, the Zariski decomposition for
curve classes admits an interesting geometric interpretation.Comment: 38 pages; revised half of the previous arXiv:1507.04316 [math.AG
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