Multiplier ideals of monomial space curves
HTML articles powered by AMS MathViewer
- by Howard M Thompson HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 1 (2014), 33-41
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).References
- Manuel Blickle, Multiplier ideals and modules on toric varieties, Math. Z. 248 (2004), no. 1, 113–121. MR 2092724, DOI 10.1007/s00209-004-0655-y
- 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, DOI 10.1112/S0024611502013801
- 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, DOI 10.1016/S1631-073X(02)02273-2
- J. A. Howald, Multiplier ideals of monomial ideals, Trans. Amer. Math. Soc. 353 (2001), no. 7, 2665–2671. MR 1828466, DOI 10.1090/S0002-9947-01-02720-9
- Reinhold Hübl and Irena Swanson, Adjoints of ideals, Michigan Math. J. 57 (2008), 447–462. Special volume in honor of Melvin Hochster. MR 2492462, DOI 10.1307/mmj/1220879418
- Amanda Ann Johnson, Multiplier ideals of determinantal ideals, ProQuest LLC, Ann Arbor, MI, 2003. Thesis (Ph.D.)–University of Michigan. MR 2704808
- Joseph Lipman, Adjoints of ideals in regular local rings, Math. Res. Lett. 1 (1994), no. 6, 739–755. With an appendix by Steven Dale Cutkosky. MR 1306018, DOI 10.4310/MRL.1994.v1.n6.a10
- 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 hypersurface singularity, Compos. Math. 143 (2007), no. 4, 1050–1068. MR 2339839, DOI 10.1112/S0010437X07002916
- Takafumi Shibuta and Shunsuke Takagi, Log canonical thresholds of binomial ideals, Manuscripta Math. 130 (2009), no. 1, 45–61. MR 2533766, DOI 10.1007/s00229-009-0270-7
- 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, DOI 10.1090/conm/448/08669
- 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
- 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, DOI 10.1017/CBO9780511756382.008
- 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, DOI 10.1090/S0002-9939-07-09177-0
- 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
- Kevin Tucker, Jumping numbers on algebraic surfaces with rational singularities, Trans. Amer. Math. Soc. 362 (2010), no. 6, 3223–3241. MR 2592954, DOI 10.1090/S0002-9947-09-04956-3
- Jarosław Włodarczyk, Simple Hironaka resolution in characteristic zero, J. Amer. Math. Soc. 18 (2005), no. 4, 779–822. MR 2163383, DOI 10.1090/S0894-0347-05-00493-5
Additional Information
- Howard M Thompson
- Affiliation: Department of Mathematics, University of Michigan-Flint, Flint, Michigan 48502-1950
- MR Author ID: 785923
- Email: hmthomps@umflint.edu
- 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
- © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- 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
- MathSciNet review: 3168880