Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Equivariant resolution of points of indeterminacy


Authors: Z. Reichstein and B. Youssin
Journal: Proc. Amer. Math. Soc. 130 (2002), 2183-2187
MSC (2000): Primary 14E15, 14L30
DOI: https://doi.org/10.1090/S0002-9939-02-06595-4
Published electronically: March 8, 2002
MathSciNet review: 1896397
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove an equivariant form of Hironaka's theorem on elimination of points of indeterminacy. Our argument uses canonical resolution of singularities and an extended version of Sumihiro's equivariant Chow lemma.


References [Enhancements On Off] (What's this?)

  • [BM] E. Bierstone, P. D. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. math. 128 (1997), no. 2, 207-302. MR 98e:14010
  • [Ha] R. Hartshorne. Algebraic geometry. Springer, 1977. MR 57:3116
  • [Hi] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic 0, I and II, Annals of Math. 79 (1964), 109-326. MR 33:7333
  • [Ka] T. Kambayashi, Projective representations of algebraic groups of transformations, Amer. J. Math. 88 (1966), 199-205. MR 34:5826
  • [MFK] D. Mumford, J. Fogarty and F. Kirwan. Geometric invariant theory. Third enlarged edition, Springer, 1994. MR 95m:14012
  • [PV] V. L. Popov, E. B. Vinberg, Invariant Theory, in Encyclopedia of Math. Sciences 55, Algebraic Geometry IV, edited by A. N. Parshin and I. R. Shafarevich, Springer-Verlag, 1994. MR 95g:14002
  • [RY1] Z. Reichstein, B. Youssin, Essential dimensions of algebraic groups and a resolution theorem for $G$-varieties, with an appendix by J. Kollár and E. Szabó, Canadian J. Math., 52, no. 5 (2000), 1018-1056. MR 2001k:14088
  • [RY2] Z. Reichstein, B. Youssin, A birational invariant for algebraic group actions, Pacific J. Math., to appear. Available at http://www.math.ubc.ca/ $\tilde{\;}$reichst/pub.html
  • [Su] H. Sumihiro, Equivariant completion, J. Math. Kyoto Univ., 14, no. 1 (1974), 1-28 MR 49:2732
  • [V] O. E. Villamayor U., Patching local uniformizations, Ann. Scient. Éc. Norm. Sup., 4e série, 25 (1992), 629-677. MR 93m:14012

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14E15, 14L30

Retrieve articles in all journals with MSC (2000): 14E15, 14L30


Additional Information

Z. Reichstein
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
Email: reichst@math.ubc.ca

B. Youssin
Affiliation: Department of Mathematics and Computer Science, University of the Negev, Be’er Sheva’, Israel
Address at time of publication: Hashofar 26/3, Ma’ale Adumim, Israel
Email: youssin@math.bgu.ac.il

DOI: https://doi.org/10.1090/S0002-9939-02-06595-4
Keywords: Group action, blowing up, resolution of singularities, equivariant map
Received by editor(s): September 29, 2000
Published electronically: March 8, 2002
Additional Notes: Z. Reichstein was partially supported by NSF grant DMS-9801675
Communicated by: Michael Stillman
Article copyright: © Copyright 2002 American Mathematical Society

American Mathematical Society