The Michigan Mathematical Journal

Adjoints of ideals

Reinhold Hübl and Irena Swanson

Full-text: Open access

Article information

Source
Michigan Math. J. Volume 57 (2008), 447-462.

Dates
First available in Project Euclid: 8 September 2008

Permanent link to this document
http://projecteuclid.org/euclid.mmj/1220879418

Digital Object Identifier
doi:10.1307/mmj/1220879418

Mathematical Reviews number (MathSciNet)
MR2492462

Zentralblatt MATH identifier
1180.13005

Subjects
Primary: 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
Secondary: 13F30: Valuation rings [See also 13A18] 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]

Citation

Hübl, Reinhold; Swanson, Irena. Adjoints of ideals. Michigan Math. J. 57 (2008), 447--462. doi:10.1307/mmj/1220879418. http://projecteuclid.org/euclid.mmj/1220879418.


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References

  • M. Blickle, M. Mustaţ\v a, and K. E. Smith, Discreteness and rationality of $F$-thresholds, arXiv:math.AG/0607660.
  • C. Ciuperca, W. Heinzer, L. Ratliff, and D. Rush, Projectively equivalent ideals and Rees valuations, J. Algebra 282 (2004), 140--156.
  • J.-P. Demailly, L. Ein, and R. Lazarsfeld, A subadditivity property of multiplier ideals, Michigan Math. J. 48 (2000), 137--156.
  • N. Hara and K. I. Yoshida, A generalization of tight closure and multiplier ideals, Trans. Amer. Math. Soc. 355 (2003), 3143--3174.
  • J. A. Howald, Multiplier ideals of monomial ideals, Trans. Amer. Math. Soc. 353 (2001), 2665--2671.
  • C. Huneke, Complete ideals in two-dimensional regular local rings, Commutative algebra (Berkeley, 1987), Math. Sci. Res. Inst. Publ., 15, pp. 325--338, Springer, New York, 1989.
  • C. Huneke and I. Swanson, Cores of ideals in 2-dimensional regular local rings, Michigan Math. J. 42 (1995), 193--208.
  • T. Järvilehto, Jumping numbers of a simple complete ideal in a two dimensional-regular local ring, Ph.D. thesis, University of Helsinki, 2007; arXiv:math.AC/0611587.
  • I. Kaplansky, $R$-sequences and homological dimension, Nagoya Math. J. 20 (1962), 195--199.
  • K. Kiyek and J. Stückrad, Integral closure of monomial ideals on regular sequences, Proceedings of the International conference on algebraic geometry and singularities (Sevilla, 2001), Rev. Mat. Iberoamericana 19 (2003), 483--508.
  • J. Lipman, Desingularization of two-dimensional schemes, Ann. of Math. (2) 107 (1978), 151--207.
  • ------, Adjoints of ideals in regular local rings, with an appendix by S. D. Cutkosky, Math. Res. Lett. 1 (1994), 739--755.
  • ------, Proximity inequalities for complete ideals in two-dimensional regular local rings, Contemp. Math., 159, pp. 293--306, Amer. Math. Soc., Providence, RI, 1994.
  • J. Lipman and A. Sathaye, Jacobian ideals and a theorem of Briançon-Skoda, Michigan Math. J. 28 (1981), 199--222.
  • J. Lipman and B. Teissier, Pseudo-local rational rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), 97--112.
  • H. Muhly and M. Sakuma, Asymptotic factorization of ideals, J. London Math. Soc. 38 (1963), 341--350.
  • L. J. Ratliff, Jr., Locally quasi-unmixed Noetherian rings and ideals of the principal class, Pacific J. Math. 52 (1974), 185--205.
  • D. Rees, Valuations associated with ideals (II), J. London Math. Soc. 31 (1956), 221--228.
  • K. E. Smith and H. M. Thompson, Irrelevant exceptional divisor for curves on a smooth surface, arXiv:math.AG/0611765.
  • I. Swanson and C. Huneke, Integral closure of ideals, rings, and modules, London Math. Soc. Lecture Note Ser., 336, Cambridge Univ. Press, Cambridge, 2006.
  • S. Takagi, Formulas for multiplier ideals on singular varieties, Amer. J. Math. 128 (2006), 1345--1362.
  • S. Takagi and K.-I. Watanabe, When does the subadditivity theorem for multiplier ideals hold? Trans. Amer. Math. Soc. 356 (2004), 3951--3961.