Upper bound of multiplicity of F-pure rings
HTML articles powered by AMS MathViewer
- by Craig Huneke and Kei-ichi Watanabe PDF
- Proc. Amer. Math. Soc. 143 (2015), 5021-5026 Request permission
Abstract:
This paper answers in the affirmative a question raised by Karl Schwede concerning an upper bound on the multiplicity of F-pure rings.References
- W. Bruns and J. Herzog, Cohen-Macauly rings, Cambridge University Press, 1997 (revised edition).
- Hubert Flenner, Divisorenklassengruppen quasihomogener Singularitäten, J. Reine Angew. Math. 328 (1981), 128–160 (German). MR 636200, DOI 10.1515/crll.1981.328.128
- Hubert Flenner, Die Sätze von Bertini für lokale Ringe, Math. Ann. 229 (1977), no. 2, 97–111 (German). MR 460317, DOI 10.1007/BF01351596
- Shiro Goto and Keiichi Watanabe, The structure of one-dimensional $F$-pure rings, J. Algebra 49 (1977), no. 2, 415–421. MR 453729, DOI 10.1016/0021-8693(77)90250-2
- Stefan Helmke, On Fujita’s conjecture, Duke Math. J. 88 (1997), no. 2, 201–216. MR 1455517, DOI 10.1215/S0012-7094-97-08807-4
- Melvin Hochster and Craig Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), no. 1, 31–116. MR 1017784, DOI 10.1090/S0894-0347-1990-1017784-6
- Craig Huneke, Hilbert functions and symbolic powers, Michigan Math. J. 34 (1987), no. 2, 293–318. MR 894879, DOI 10.1307/mmj/1029003560
- Craig Huneke and Irena Swanson, Integral closure of ideals, rings, and modules, London Mathematical Society Lecture Note Series, vol. 336, Cambridge University Press, Cambridge, 2006. MR 2266432
- Joseph Lipman, Rational singularities, with applications to algebraic surfaces and unique factorization, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 195–279. MR 276239
- Joseph Lipman and Bernard Teissier, Pseudorational local rings and a theorem of Briançon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), no. 1, 97–116. MR 600418
- Karl Schwede and Kevin Tucker, On the number of compatibly Frobenius split subvarieties, prime $F$-ideals, and log canonical centers, Ann. Inst. Fourier (Grenoble) 60 (2010), no. 5, 1515–1531 (English, with English and French summaries). MR 2766221
- Karl Schwede and Wenliang Zhang, Bertini theorems for $F$-singularities, Proc. Lond. Math. Soc. (3) 107 (2013), no. 4, 851–874. MR 3108833, DOI 10.1112/plms/pdt007
- Richard P. Stanley, The upper bound conjecture and Cohen-Macaulay rings, Studies in Appl. Math. 54 (1975), no. 2, 135–142. MR 458437, DOI 10.1002/sapm1975542135
- Keiichi Watanabe, Rational singularities with $k^{\ast }$-action, Commutative algebra (Trento, 1981) Lecture Notes in Pure and Appl. Math., vol. 84, Dekker, New York, 1983, pp. 339–351. MR 686954
Additional Information
- Craig Huneke
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904
- MR Author ID: 89875
- Email: huneke@virginia.edu
- Kei-ichi Watanabe
- Affiliation: Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo 156–0045, Japan
- MR Author ID: 216208
- Email: watanabe@math.chs.nihon-u.ac.jp
- Received by editor(s): June 27, 2013
- Received by editor(s) in revised form: August 29, 2013
- Published electronically: August 5, 2015
- Additional Notes: The first author was partially supported by NSF grant 1259142
The second author was partially supported by Grant-in-Aid for Scientific Research 20540050 and Individual Research Expense of College of Humanity and Sciences, Nihon University
The authors thank AIM for the opportunity to work together. - Communicated by: Irena Peeva
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 5021-5026
- MSC (2010): Primary 13H15; Secondary 13C99, 14B05
- DOI: https://doi.org/10.1090/proc/12851
- MathSciNet review: 3411123