Algebraic bounds on analytic multiplier ideals

Brian Lehmann[1]

  • [1] Rice University Department of Mathematics Houston, TX 77005 (USA)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 3, page 1077-1108
  • ISSN: 0373-0956

Abstract

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Given a pseudo-effective divisor L we construct the diminished ideal 𝒥 σ ( 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 ( h min ) of the metric of minimal singularities on 𝒪 X ( L ) is contained in 𝒥 σ ( L ) . We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.

How to cite

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Lehmann, Brian. "Algebraic bounds on analytic multiplier ideals." Annales de l’institut Fourier 64.3 (2014): 1077-1108. <http://eudml.org/doc/275477>.

@article{Lehmann2014,
abstract = {Given a pseudo-effective divisor $L$ we construct the diminished ideal $\mathcal\{J\}_\{\sigma \}(L)$, 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 $\mathcal\{J\}(h_\{\textrm\{min\}\})$ of the metric of minimal singularities on $\mathcal\{O\}_\{X\}(L)$ is contained in $\mathcal\{J\}_\{\sigma \}(L)$. We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.},
affiliation = {Rice University Department of Mathematics Houston, TX 77005 (USA)},
author = {Lehmann, Brian},
journal = {Annales de l’institut Fourier},
keywords = {Multiplier ideals; metric of minimal singularities; multiplier ideals},
language = {eng},
number = {3},
pages = {1077-1108},
publisher = {Association des Annales de l’institut Fourier},
title = {Algebraic bounds on analytic multiplier ideals},
url = {http://eudml.org/doc/275477},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Lehmann, Brian
TI - Algebraic bounds on analytic multiplier ideals
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 3
SP - 1077
EP - 1108
AB - Given a pseudo-effective divisor $L$ we construct the diminished ideal $\mathcal{J}_{\sigma }(L)$, 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 $\mathcal{J}(h_{\textrm{min}})$ of the metric of minimal singularities on $\mathcal{O}_{X}(L)$ is contained in $\mathcal{J}_{\sigma }(L)$. We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.
LA - eng
KW - Multiplier ideals; metric of minimal singularities; multiplier ideals
UR - http://eudml.org/doc/275477
ER -

References

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