Asymptotic invariants of base loci

Ein, Lawrence; Lazarsfeld, Robert; Mustaţă, Mircea; Nakamaye, Michael; Popa, Mihnea

doi:10.5802/aif.2225

Cited by 186 publications

(203 citation statements)

References 15 publications

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“…This notation was established in [4] for projective varieties, but we will use it in a slightly more general setting; see for example [11]. A log pair (X, ∆) is a normal variety X and an R-Weil divisor ∆ ≥ 0 such that K X +∆ is R-Cartier.…”

Section: B(d + A)mentioning

confidence: 99%

Existence of minimal models for varieties of log general type II

Hacon

M$^{\textup{c}}$Kernan

2009

J. Amer. Math. Soc.

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Section: B(d + A)mentioning

confidence: 99%

Existence of minimal models for varieties of log general type II

Hacon

M$^{\textup{c}}$Kernan

2009

J. Amer. Math. Soc.

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“…By choosing H sufficiently small, we may assume that H = εA−H is ample. Therefore, we may assume that the pair (X, B + See [8,7,14,20], etc for more details on the non-ample and non-nef loci.…”

Section: Introductionmentioning

confidence: 99%

Duality of the cones of divisors and curves

Choi¹

2012

Mathematical Research Letters

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“…It is checked in [13] that B − (L) ⊂ B R (L) and that the diminished base locus only depends on the numerical class of L. In some sense the diminished base locus measures the failure of L to be nef.…”

Section: R-divisorsmentioning

confidence: 99%

Algebraic bounds on analytic multiplier ideals

Lehmann¹

2014

Annales De l'Institut Fourier

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Given a pseudo-effective divisor L we construct the diminished ideal Jσ(L), a "continuous" extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. Our main theorem shows that for most pseudo-effective divisors L the multiplier ideal J (hmin) of the metric of minimal singularities on OX (L) is contained in Jσ(L). We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.

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Asymptotic invariants of base loci

Cited by 186 publications

References 15 publications

Existence of minimal models for varieties of log general type II

Existence of minimal models for varieties of log general type II

Duality of the cones of divisors and curves

Algebraic bounds on analytic multiplier ideals

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