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A note on Mustaţă's computation of multiplier ideals of hyperplane arrangements
Author(s):
Zach
Teitler
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1575-1579.
MSC (2000):
Primary 14B05;
Secondary 52C35
Posted:
November 30, 2007
MathSciNet review:
2373586
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Abstract:
In 2006, M. Mustaţă used jet schemes to compute the multiplier ideals of reduced hyperplane arrangements. We give a simpler proof using a log resolution and generalize to non-reduced arrangements. By applying the idea of wonderful models introduced by De Concini-Procesi in 1995, we also simplify the result. Indeed, Mustaţă's result expresses the multiplier ideal as an intersection, and our result uses (generally) fewer terms in the intersection.
References:
-
- 1.
- C. De Concini and C. Procesi.
Wonderful models of subspace arrangements.
Selecta Math. (N.S.), 1(3):459-494, 1995. MR 1366622 (97k:14013) - 2.
- Eva Maria Feichtner.
De Concini-Procesi wonderful arrangement models: a discrete geometer's point of view.
In Combinatorial and computational geometry, volume 52 of Math. Sci. Res. Inst. Publ., pages 333-360. Cambridge Univ. Press, Cambridge, 2005. MR 2178326 (2006i:05178) - 3.
- Robin Hartshorne.
Algebraic geometry.
Springer-Verlag, New York, 1977.
Graduate Texts in Mathematics, No. 52. MR 0463157 (57:3116) - 4.
- Yi Hu.
A compactification of open varieties.
Trans. Amer. Math. Soc., 355(12):4737-4753 (electronic), 2003. MR 1997581 (2004d:14080) - 5.
- Robert Lazarsfeld.
Positivity in algebraic geometry. II, volume 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics].
Springer-Verlag, Berlin, 2004.
Positivity for vector bundles, and multiplier ideals. MR 2095472 (2005k:14001b) - 6.
- Li Li.
Wonderful compactifications of arrangements of subvarieties, November 2006.
http://front.math.ucdavis.edu/math.AG/0611412 arXiv:math.AG/0611412. - 7.
- Mircea Mustaţa.
Multiplier ideals of hyperplane arrangements.
Trans. Amer. Math. Soc., 358:5015-5023, 2006. MR 2231883 (2007d:14007) - 8.
- Morihiko Saito.
Multiplier ideals, b-function, and spectrum of a hyperplane singularity.
http://front.math.ucdavis.edu/math.AG/0402363 arXiv:math.A G/0402363, December 2006. - 9.
- N. J. A. Sloane.
The On-Line Encyclopedia of Integer Sequences, 2006.
Published electronically at http://www.research.att.com/ njas/sequences/A000110. - 10.
- Zachariah C. Teitler.
Multiplier ideals of general line arrangements in  .
Comm. Algebra (to appear), 2007.
Also available at http://front.math.ucdavis.edu/math.AG/0508308 arXiv:math.A G/0508308. MR 2324623
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Additional Information:
Zach
Teitler
Affiliation:
Department of Mathematics, Southeastern Louisiana University, SLU 10687, Hammond, Louisiana 70401
Email:
zteitler@selu.edu
DOI:
10.1090/S0002-9939-07-09177-0
PII:
S 0002-9939(07)09177-0
Keywords:
Multiplier ideals,
hyperplane arrangements,
wonderful models
Received by editor(s):
October 12, 2006
Received by editor(s) in revised form:
March 1, 2007
Posted:
November 30, 2007
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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