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

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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.

**[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**-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/``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**

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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