Spectrum and multiplier ideals of arbitrary subvarieties

Alexandru Dimca[1]; Philippe Maisonobe[1]; Morihiko Saito[2]

  • [1] Université de Nice-Sophia Antipolis Laboratoire J.A. Dieudonné, UMR du CNRS 6621 Parc Valrose 06108 Nice Cedex 02 (France)
  • [2] RIMS Kyoto University Kyoto 606–8502 (Japan)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 4, page 1633-1653
  • ISSN: 0373-0956

Abstract

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We introduce a spectrum for arbitrary subvarieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for the coefficients of integral exponents. We show a relation to the graded pieces of the multiplier ideals by using the filtration V of Kashiwara and Malgrange. This implies a partial generalization of a theorem of Budur in the hypersurface case. The key point is to consider the direct sum of the graded pieces of the multiplier ideals as a module over the algebra defining the normal cone of the subvariety. We also give a combinatorial description in the case of monomial ideals.

How to cite

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Dimca, Alexandru, Maisonobe, Philippe, and Saito, Morihiko. "Spectrum and multiplier ideals of arbitrary subvarieties." Annales de l’institut Fourier 61.4 (2011): 1633-1653. <http://eudml.org/doc/219795>.

@article{Dimca2011,
abstract = {We introduce a spectrum for arbitrary subvarieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for the coefficients of integral exponents. We show a relation to the graded pieces of the multiplier ideals by using the filtration V of Kashiwara and Malgrange. This implies a partial generalization of a theorem of Budur in the hypersurface case. The key point is to consider the direct sum of the graded pieces of the multiplier ideals as a module over the algebra defining the normal cone of the subvariety. We also give a combinatorial description in the case of monomial ideals.},
affiliation = {Université de Nice-Sophia Antipolis Laboratoire J.A. Dieudonné, UMR du CNRS 6621 Parc Valrose 06108 Nice Cedex 02 (France); Université de Nice-Sophia Antipolis Laboratoire J.A. Dieudonné, UMR du CNRS 6621 Parc Valrose 06108 Nice Cedex 02 (France); RIMS Kyoto University Kyoto 606–8502 (Japan)},
author = {Dimca, Alexandru, Maisonobe, Philippe, Saito, Morihiko},
journal = {Annales de l’institut Fourier},
keywords = {Spectrum; V-filtration; multiplier ideal; spectrum; -filtration; -function},
language = {eng},
number = {4},
pages = {1633-1653},
publisher = {Association des Annales de l’institut Fourier},
title = {Spectrum and multiplier ideals of arbitrary subvarieties},
url = {http://eudml.org/doc/219795},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Dimca, Alexandru
AU - Maisonobe, Philippe
AU - Saito, Morihiko
TI - Spectrum and multiplier ideals of arbitrary subvarieties
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 4
SP - 1633
EP - 1653
AB - We introduce a spectrum for arbitrary subvarieties. This generalizes the definition by Steenbrink for hypersurfaces. In the isolated complete intersection singularity case, it coincides with the one given by Ebeling and Steenbrink except for the coefficients of integral exponents. We show a relation to the graded pieces of the multiplier ideals by using the filtration V of Kashiwara and Malgrange. This implies a partial generalization of a theorem of Budur in the hypersurface case. The key point is to consider the direct sum of the graded pieces of the multiplier ideals as a module over the algebra defining the normal cone of the subvariety. We also give a combinatorial description in the case of monomial ideals.
LA - eng
KW - Spectrum; V-filtration; multiplier ideal; spectrum; -filtration; -function
UR - http://eudml.org/doc/219795
ER -

References

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