F-blowups of F-regular surface singularities
HTML articles powered by AMS MathViewer
- by Nobuo Hara PDF
- Proc. Amer. Math. Soc. 140 (2012), 2215-2226 Request permission
Abstract:
We prove that F-blowups of any F-regular surface singularity coincide with the minimal resolution.References
- Michael Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962), 485–496. MR 146182, DOI 10.2307/2372985
- M. Artin, Coverings of the rational double points in characteristic $p$, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 11–22. MR 0450263
- M. Artin and J.-L. Verdier, Reflexive modules over rational double points, Math. Ann. 270 (1985), no. 1, 79–82. MR 769609, DOI 10.1007/BF01455531
- Maurice Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc. 293 (1986), no. 2, 511–531. MR 816307, DOI 10.1090/S0002-9947-1986-0816307-7
- Wolf P. Barth, Klaus Hulek, Chris A. M. Peters, and Antonius Van de Ven, Compact complex surfaces, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 4, Springer-Verlag, Berlin, 2004. MR 2030225, DOI 10.1007/978-3-642-57739-0
- G. Gonzalez-Sprinberg and J.-L. Verdier, Construction géométrique de la correspondance de McKay, Ann. Sci. École Norm. Sup. (4) 16 (1983), no. 3, 409–449 (1984) (French). MR 740077, DOI 10.24033/asens.1454
- Nobuo Hara, Classification of two-dimensional $F$-regular and $F$-pure singularities, Adv. Math. 133 (1998), no. 1, 33–53. MR 1492785, DOI 10.1006/aima.1997.1682
- Hara, N. and Sawada, T., Splitting of Frobenius sandwiches, RIMS Kôkyûroku Bessatsu B24 (2011), 121–141.
- Nobuo Hara and Kei-Ichi Watanabe, F-regular and F-pure rings vs. log terminal and log canonical singularities, J. Algebraic Geom. 11 (2002), no. 2, 363–392. MR 1874118, DOI 10.1090/S1056-3911-01-00306-X
- Melvin Hochster and Craig Huneke, Tight closure and strong $F$-regularity, Mém. Soc. Math. France (N.S.) 38 (1989), 119–133. Colloque en l’honneur de Pierre Samuel (Orsay, 1987). MR 1044348
- Craig Huneke, Tight closure and its applications, CBMS Regional Conference Series in Mathematics, vol. 88, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1996. With an appendix by Melvin Hochster. MR 1377268, DOI 10.1016/0167-4889(95)00136-0
- Akira Ishii, On the McKay correspondence for a finite small subgroup of $\textrm {GL}(2,\Bbb C)$, J. Reine Angew. Math. 549 (2002), 221–233. MR 1916656, DOI 10.1515/crll.2002.064
- Yujiro Kawamata, Index 1 covers of log terminal surface singularities, J. Algebraic Geom. 8 (1999), no. 3, 519–527. MR 1689354
- Lee, Y. and Nakayama, N., Simply connected surfaces of general type in positive characteristic via deformation theory, preprint.
- Anurag K. Singh, $\mathbf Q$-Gorenstein splinter rings of characteristic $p$ are F-regular, Math. Proc. Cambridge Philos. Soc. 127 (1999), no. 2, 201–205. MR 1735920, DOI 10.1017/S0305004199003710
- Gerhard Seibert, The Hilbert-Kunz function of rings of finite Cohen-Macaulay type, Arch. Math. (Basel) 69 (1997), no. 4, 286–296. MR 1466822, DOI 10.1007/s000130050123
- Karen E. Smith and Michel Van den Bergh, Simplicity of rings of differential operators in prime characteristic, Proc. London Math. Soc. (3) 75 (1997), no. 1, 32–62. MR 1444312, DOI 10.1112/S0024611597000257
- Yukinobu Toda and Takehiko Yasuda, Noncommutative resolution, $\textrm {F}$-blowups and $D$-modules, Adv. Math. 222 (2009), no. 1, 318–330. MR 2531377, DOI 10.1016/j.aim.2009.04.004
- Jürgen Wunram, Reflexive modules on quotient surface singularities, Math. Ann. 279 (1988), no. 4, 583–598. MR 926422, DOI 10.1007/BF01458530
- Yasuda, T., Universal flattening of Frobenius, to appear in the Proceedings of the 5th Franco-Japanese symposium on singularities, 2009.
- Takehiko Yasuda, On monotonicity of $F$-blowup sequences, Illinois J. Math. 53 (2009), no. 1, 101–110. MR 2584937
Additional Information
- Nobuo Hara
- Affiliation: Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
- Email: hara@math.tohoku.ac.jp
- Received by editor(s): December 23, 2010
- Received by editor(s) in revised form: February 14, 2011
- Published electronically: October 24, 2011
- Additional Notes: The author is partially supported by Grant-in-Aid for Scientific Research, JSPS
- Communicated by: Lev Borisov
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2215-2226
- MSC (2010): Primary 13A35, 14B05
- DOI: https://doi.org/10.1090/S0002-9939-2011-11074-8
- MathSciNet review: 2898685