Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

F-blowups of F-regular surface singularities

Author: Nobuo Hara
Journal: Proc. Amer. Math. Soc. 140 (2012), 2215-2226
MSC (2010): Primary 13A35, 14B05
Posted: October 24, 2011
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that F-blowups of any F-regular surface singularity coincide with the minimal resolution.

References

[Ar1] Michael Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer. J. Math. 84 (1962), 485–496. MR 0146182 (26 #3704)
[Ar2] 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 (56 #8559)
[AV] M. Artin and J.-L. Verdier, Reflexive modules over rational double points, Math. Ann. 270 (1985), no. 1, 79–82. MR 769609 (85m:14006), http://dx.doi.org/10.1007/BF01455531
[Aus] Maurice Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc. 293 (1986), no. 2, 511–531. MR 816307 (87e:16073), http://dx.doi.org/10.1090/S0002-9947-1986-0816307-7
[BHPV] 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 (2004m:14070)
[GSV] 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 (85k:14019)
[H] Nobuo Hara, Classification of two-dimensional 𝐹-regular and 𝐹-pure singularities, Adv. Math. 133 (1998), no. 1, 33–53. MR 1492785 (99a:14048), http://dx.doi.org/10.1006/aima.1997.1682
[HS] Hara, N. and Sawada, T., Splitting of Frobenius sandwiches, RIMS Kôkyûroku Bessatsu B24 (2011), 121-141.
[HW] 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 (2002k:13009), http://dx.doi.org/10.1090/S1056-3911-01-00306-X
[HH] 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 (91i:13025)
[Hu] 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, 1996. With an appendix by Melvin Hochster. MR 1377268 (96m:13001)
[I] Akira Ishii, On the McKay correspondence for a finite small subgroup of 𝐺𝐿(2,ℂ), J. Reine Angew. Math. 549 (2002), 221–233. MR 1916656 (2003d:14021), http://dx.doi.org/10.1515/crll.2002.064
[K] Yujiro Kawamata, Index 1 covers of log terminal surface singularities, J. Algebraic Geom. 8 (1999), no. 3, 519–527. MR 1689354 (2001f:14066)
[LN] Lee, Y. and Nakayama, N., Simply connected surfaces of general type in positive characteristic via deformation theory, preprint.
[Si] Anurag K. Singh, 𝐐-Gorenstein splinter rings of characteristic 𝐩 are F-regular, Math. Proc. Cambridge Philos. Soc. 127 (1999), no. 2, 201–205. MR 1735920 (2000j:13006), http://dx.doi.org/10.1017/S0305004199003710
[Sei] Gerhard Seibert, The Hilbert-Kunz function of rings of finite Cohen-Macaulay type, Arch. Math. (Basel) 69 (1997), no. 4, 286–296. MR 1466822 (98h:13022), http://dx.doi.org/10.1007/s000130050123
[SVdB] 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 (98d:16039), http://dx.doi.org/10.1112/S0024611597000257
[TY] Yukinobu Toda and Takehiko Yasuda, Noncommutative resolution, 𝐹-blowups and 𝐷-modules, Adv. Math. 222 (2009), no. 1, 318–330. MR 2531377 (2011b:14005), http://dx.doi.org/10.1016/j.aim.2009.04.004
[W] Jürgen Wunram, Reflexive modules on quotient surface singularities, Math. Ann. 279 (1988), no. 4, 583–598. MR 926422 (89g:14029), http://dx.doi.org/10.1007/BF01458530
[Y1] Yasuda, T., Universal flattening of Frobenius, to appear in the Proceedings of the 5th Franco-Japanese symposium on singularities, 2009.
[Y2] Takehiko Yasuda, On monotonicity of 𝐹-blowup sequences, Illinois J. Math. 53 (2009), no. 1, 101–110. MR 2584937 (2011b:14007)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|