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Multiplier ideals of monomial space curves


Author: Howard M Thompson
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 33-41
MSC (2010): Primary 14F18; Secondary 14H50, 14M25
DOI: https://doi.org/10.1090/S2330-1511-2014-00001-8
Published electronically: February 26, 2014
MathSciNet review: 3168880
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Abstract: This paper presents a formula for the multiplier ideals of a monomial space curve. The formula is obtained from a careful choice of log resolution. We construct a toric blowup of affine space in such a way that a log resolution of the monomial curve may be constructed from this toric variety in a well controlled manner. The construction exploits a theorem of González Pérez and Teissier (2002).


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  • [1] Manuel Blickle, Multiplier ideals and modules on toric varieties, Math. Z. 248 (2004), no. 1, 113-121. MR 2092724 (2006a:14082), https://doi.org/10.1007/s00209-004-0655-y
  • [2] A. Bravo and O. Villamayor U., A strengthening of resolution of singularities in characteristic zero, Proc. London Math. Soc. (3) 86 (2003), no. 2, 327-357. MR 1971154 (2004c:14020), https://doi.org/10.1112/S0024611502013801
  • [3] Pedro Daniel González Pérez and Bernard Teissier, Embedded resolutions of non necessarily normal affine toric varieties, C. R. Math. Acad. Sci. Paris 334 (2002), no. 5, 379-382 (English, with English and French summaries). MR 1892938 (2003b:14019), https://doi.org/10.1016/S1631-073X(02)02273-2
  • [4] J. A. Howald, Multiplier ideals of monomial ideals, Trans. Amer. Math. Soc. 353 (2001), no. 7, 2665-2671 (electronic). MR 1828466 (2002b:14061), https://doi.org/10.1090/S0002-9947-01-02720-9
  • [5] Reinhold Hübl and Irena Swanson, Adjoints of ideals, Special volume in honor of Melvin Hochster, Michigan Math. J. 57 (2008), 447-462. MR 2492462 (2010a:13003), https://doi.org/10.1307/mmj/1220879418
  • [6] Amanda Ann Johnson, Multiplier ideals of determinantal ideals, ProQuest LLC, Ann Arbor, MI, 2003. Thesis (Ph.D.)-University of Michigan. MR 2704808
  • [7] Joseph Lipman, Adjoints of ideals in regular local rings, with an appendix by Steven Dale Cutkosky, Math. Res. Lett. 1 (1994), no. 6, 739-755. MR 1306018 (95k:13028)
  • [8] Mircea Mustaţă, Multiplier ideals of hyperplane arrangements, Trans. Amer. Math. Soc. 358 (2006), no. 11, 5015-5023 (electronic). MR 2231883 (2007d:14007), https://doi.org/10.1090/S0002-9947-06-03895-5
  • [9] Morihiko Saito, Multiplier ideals, $ b$-function, and spectrum of a hypersurface singularity, Compos. Math. 143 (2007), no. 4, 1050-1068. MR 2339839 (2008h:32042)
  • [10] Takafumi Shibuta and Shunsuke Takagi, Log canonical thresholds of binomial ideals, Manuscripta Math. 130 (2009), no. 1, 45-61. MR 2533766 (2010j:14031), https://doi.org/10.1007/s00229-009-0270-7
  • [11] Karen E. Smith and Howard M. Thompson, Irrelevant exceptional divisors for curves on a smooth surface, Algebra, geometry and their interactions, Contemp. Math., vol. 448, Amer. Math. Soc., Providence, RI, 2007, pp. 245-254. MR 2389246 (2009c:14004), https://doi.org/10.1090/conm/448/08669
  • [12] Bernard Teissier, Valuations, deformations, and toric geometry, Valuation theory and its applications, Vol. II (Saskatoon, SK, 1999), Fields Inst. Commun., vol. 33, Amer. Math. Soc., Providence, RI, 2003, pp. 361-459. MR 2018565 (2005m:14021)
  • [13] Bernard Teissier, Monomial ideals, binomial ideals, polynomial ideals, Trends in commutative algebra, Math. Sci. Res. Inst. Publ., vol. 51, Cambridge Univ. Press, Cambridge, 2004, pp. 211-246. MR 2132653 (2006c:13032), https://doi.org/10.1017/CBO9780511756382.008
  • [14] Zach Teitler, A note on Mustaţă's computation of multiplier ideals of hyperplane arrangements, Proc. Amer. Math. Soc. 136 (2008), no. 5, 1575-1579. MR 2373586 (2008k:14005), https://doi.org/10.1090/S0002-9939-07-09177-0
  • [15] Zachariah C. Teitler, Multiplier ideals of general line arrangements in $ \mathbb{C}^3$, Comm. Algebra 35 (2007), no. 6, 1902-1913. MR 2324623 (2008e:14003), https://doi.org/10.1080/00927870701247005
  • [16] Kevin Tucker, Jumping numbers on algebraic surfaces with rational singularities, Trans. Amer. Math. Soc. 362 (2010), no. 6, 3223-3241. MR 2592954 (2011c:14106), https://doi.org/10.1090/S0002-9947-09-04956-3
  • [17] Jarosław Włodarczyk, Simple Hironaka resolution in characteristic zero, J. Amer. Math. Soc. 18 (2005), no. 4, 779-822 (electronic). MR 2163383 (2006f:14014), https://doi.org/10.1090/S0894-0347-05-00493-5

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Additional Information

Howard M Thompson
Affiliation: Department of Mathematics, University of Michigan-Flint, Flint, Michigan 48502-1950
Email: hmthomps@umflint.edu

DOI: https://doi.org/10.1090/S2330-1511-2014-00001-8
Received by editor(s): June 15, 2010
Received by editor(s) in revised form: April 26, 2012
Published electronically: February 26, 2014
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)

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