A note on Mustata’s computation of multiplier ideals of hyperplane arrangements
HTML articles powered by AMS MathViewer
- by Zach Teitler
- Proc. Amer. Math. Soc. 136 (2008), 1575-1579
- DOI: https://doi.org/10.1090/S0002-9939-07-09177-0
- Published electronically: November 30, 2007
- PDF | Request permission
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
- C. De Concini and C. Procesi, Wonderful models of subspace arrangements, Selecta Math. (N.S.) 1 (1995), no. 3, 459–494. MR 1366622, DOI 10.1007/BF01589496
- Eva Maria Feichtner, De Concini-Procesi wonderful arrangement models: a discrete geometer’s point of view, Combinatorial and computational geometry, Math. Sci. Res. Inst. Publ., vol. 52, Cambridge Univ. Press, Cambridge, 2005, pp. 333–360. MR 2178326
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Yi Hu, A compactification of open varieties, Trans. Amer. Math. Soc. 355 (2003), no. 12, 4737–4753. MR 1997581, DOI 10.1090/S0002-9947-03-03247-1
- Robert Lazarsfeld, Positivity in algebraic geometry. I, 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], vol. 48, Springer-Verlag, Berlin, 2004. Classical setting: line bundles and linear series. MR 2095471, DOI 10.1007/978-3-642-18808-4
- Li Li. Wonderful compactifications of arrangements of subvarieties, November 2006. http://front.math.ucdavis.edu/math.AG/0611412 arXiv:math.AG/0611412.
- Mircea Mustaţă, Multiplier ideals of hyperplane arrangements, Trans. Amer. Math. Soc. 358 (2006), no. 11, 5015–5023. MR 2231883, DOI 10.1090/S0002-9947-06-03895-5
- 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.
- N. J. A. Sloane. The On-Line Encyclopedia of Integer Sequences, 2006. Published electronically at http://www.research.att.com/ njas/sequences/A000110.
- Zachariah C. Teitler, Multiplier ideals of general line arrangements in $\Bbb C^3$, Comm. Algebra 35 (2007), no. 6, 1902–1913. MR 2324623, DOI 10.1080/00927870701247005
Bibliographic Information
- Zach Teitler
- Affiliation: Department of Mathematics, Southeastern Louisiana University, SLU 10687, Hammond, Louisiana 70401
- MR Author ID: 788722
- ORCID: 0000-0003-2579-9173
- Email: zteitler@selu.edu
- Received by editor(s): October 12, 2006
- Received by editor(s) in revised form: March 1, 2007
- Published electronically: November 30, 2007
- Communicated by: Bernd Ulrich
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1575-1579
- MSC (2000): Primary 14B05; Secondary 52C35
- DOI: https://doi.org/10.1090/S0002-9939-07-09177-0
- MathSciNet review: 2373586