F-Thresholds, tight closure, integral closure, and multiplicity bounds
Craig Huneke, Mircea Mustata, Shunsuke Takagi, and Ken-ichi Watanabe
Source: Michigan Math. J. Volume 57
(2008), 463-483.
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References
I. M. Aberbach, Extensions of weakly and strongly F-regular rings by flat maps, J. Algebra 241 (2001), 799--807.
Mathematical Reviews (MathSciNet): MR1843326
Digital Object Identifier: doi:10.1006/jabr.2001.8785
I. M. Aberbach and C. Huneke, F-rational rings and the integral closures of ideals, Michigan Math. J. 49 (2001), 3--11.
Mathematical Reviews (MathSciNet): MR1827071
Digital Object Identifier: doi:10.1307/mmj/1008719031
Project Euclid: euclid.mmj/1008719031
M. Blickle, M. Mustaţă, and K. E. Smith, Discreteness and rationality of F-thresholds, Michigan Math. J. 57 (2008), 43--61.
------, F-thresholds of hypersurfaces, Trans. Amer. Math. Soc. (to appear).
A. Corti, Singularities of linear systems and 3-fold birational geometry, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., 281, pp. 259--312, Cambridge Univ. Press, Cambridge, 2000.
Mathematical Reviews (MathSciNet): MR1798984
Zentralblatt MATH: 0960.14017
T. de Fernex, Length, multiplicity, and multiplier ideals, Trans. Amer. Math. Soc. 358 (2006), 3717--3731.
Mathematical Reviews (MathSciNet): MR2218996
Digital Object Identifier: doi:10.1090/S0002-9947-06-03862-1
T. de Fernex, L. Ein, and M. Mustaţă, Bounds for log canonical threshold with applications to birational rigidity, Math. Res. Lett. 10 (2003), 219--236.
Mathematical Reviews (MathSciNet): MR1981899
------, Multiplicities and log canonical threshold, J. Algebraic Geom. 13 (2004), 603--615.
Mathematical Reviews (MathSciNet): MR2047683
D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Grad. Texts in Math., 150, Springer-Verlag, New York, 1995.
Mathematical Reviews (MathSciNet): MR1322960
Zentralblatt MATH: 0819.13001
R. Fedder and K.-i. Watanabe, A characterization of F-regularity in terms of F-purity, Commutative algebra (Berkeley, 1987), Math. Sci. Res. Inst. Publ., 15, pp. 227--245, Springer-Verlag, New York, 1989.
Mathematical Reviews (MathSciNet): MR1015520
Zentralblatt MATH: 0738.13004
N. Hara, F-pure thresholds and F-jumping exponents in dimension two, with an appendix by P. Monsky, Math. Res. Lett. 13 (2006), 747--760.
Mathematical Reviews (MathSciNet): MR2280772
N. Hara and S. Takagi, On a generalization of test ideals, Nagoya Math. J. 175 (2004), 59--74.
Mathematical Reviews (MathSciNet): MR2085311
Project Euclid: euclid.nmj/1114632095
N. Hara and K. Yoshida, A generalization of tight closure and multiplier ideals, Trans. Amer. Math. Soc. 355 (2003), 3143--3174.
Mathematical Reviews (MathSciNet): MR1974679
Digital Object Identifier: doi:10.1090/S0002-9947-03-03285-9
JSTOR: links.jstor.org
M. Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math. J. 51 (1973), 25--43.
Mathematical Reviews (MathSciNet): MR349656
Project Euclid: euclid.nmj/1118794784
M. Hochster and C. Huneke, Tight closure, invariant theory and the Briançon--Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31--116.
Mathematical Reviews (MathSciNet): MR1017784
Digital Object Identifier: doi:10.2307/1990984
JSTOR: links.jstor.org
C. Huneke, Tight closure and its applications, with an appendix by M. Hochster, CBMS Reg. Conf. Ser. Math., 88, Amer. Math. Soc., Providence, RI, 1996.
Mathematical Reviews (MathSciNet): MR1377268
Zentralblatt MATH: 0930.13004
E. Hyry and U. O. Villamayor, A Briançon--Skoda theorem for isolated singularities, J. Algebra 204 (1998), 656--665.
Mathematical Reviews (MathSciNet): MR1624420
Digital Object Identifier: doi:10.1006/jabr.1997.7386
M. Katzman, G. Lyubeznik, and W. Zhang, On the discreteness and rationality of jumping coefficients, preprint, arxiv: 0706.3028.
R. Lazarsfeld, Positivity in algebraic geometry II, Ergeb. Math. Grenzgeb. (3), 49, Springer-Verlag, Berlin, 2004.
Mathematical Reviews (MathSciNet): MR2095472
D. Mumford, Stability of projective varieties, Enseign. Math. (2) 23 (1977), 39--110.
Mathematical Reviews (MathSciNet): MR450272
M. Mustaţă, S. Takagi, and K.-i. Watanabe, F-thresholds and Bernstein--Sato polynomials, Proceedings of the fourth European congress of mathematics, pp. 341--364, European Mathematical Society, Zürich, 2005.
Mathematical Reviews (MathSciNet): MR2185754
C. Peskine and L. Szpiro, Liaison des variétés algébriques I, Invent. Math. 26 (1974), 271--302.
Mathematical Reviews (MathSciNet): MR364271
Digital Object Identifier: doi:10.1007/BF01425554
S. Takagi and K.-i. Watanabe, On F-pure thresholds, J. Algebra 282 (2004), 278--297.
Mathematical Reviews (MathSciNet): MR2097584
Digital Object Identifier: doi:10.1016/j.jalgebra.2004.07.011
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