|
The Hironaka theorem on resolution of singularities
(Or: A proof we always wanted to understand)
Author:
Herwig Hauser
Journal:
Bull. Amer. Math. Soc. 40 (2003), 323-403
MSC (2000):
Primary 14B05, 14E15, 32S05, 32S10, 32S45
Posted:
May 6, 2003
MathSciNet review:
1978567
Full-text PDF
Abstract |
References |
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Additional Information
Abstract: This paper is a handyman's manual for learning how to resolve the singularities of algebraic varieties defined over a field of characteristic zero by sequences of blowups.
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References directly related to the Hironaka Theorem
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- Aroca, J.-M., Hironaka, H., Vicente, J.-L.: The theory of the maximal contact. Memorias Mat. Inst. Jorge Juan, Madrid 29 (1975). MR 56:3344
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- Aroca, J.-M., Hironaka, H., Vicente, J.-L.: Desingularization theorems. Memorias Mat. Inst. Jorge Juan, Madrid 29 (1975). MR 80h:32027
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- Bravo, A., Encinas, S., Villamayor, O.: A simplified proof of desingularization and applications. Preprint. Download at http://arXiv.org/archive/math, math.AG/0206244.
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- Bierstone, E., Milman, P.: Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant. Invent. Math. 128 (1997), 207-302. MR 98e:14010
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- Bierstone, E., Milman, P.: Uniformization of analytic spaces. J. Amer. Math. Soc. 2 (1989), 801-836. MR 91c:32033
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- Bierstone, E., Milman, P.: Semianalytic and subanalytic sets. Publ. Math. IHES 67 (1988), 5-42. MR 89k:32011
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- Bierstone, E., Milman, P.: Desingularization algorithms I. The role of exceptional divisors. Preprint. Download at http://arXiv.org/archive/math, math.AG/0207098.
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- Bodnár, G.: Algorithmic resolution of singularities. Thesis, Univ. Linz, 2001.
- [Bo2]
- Bodnár, G.: Computation of blowing up centers. J. Pure Appl. Alg. 179 (2003), 221-233.
- [Bo3]
- Bodnár, G.: Algorithmic tests for the normal crossings property. Preprint, Univ. Linz.
- [BS1]
- Bodnár, G., Schicho, J.: Automated Resolution of Singularities for Hypersurfaces. J. Symb. Comp. 30 (2000), 401-428. MR 2001i:14083
- [BS 2]
- Bodnár, G., Schicho, J.: Two computational techniques for singularity resolution. J. Symbolic Comput. 32 (2001), no. 1-2, 39-54. MR 2002d:14020
- [BS 3]
- Bodnár, G., Schicho, J.: A computer program for the resolution of singularities. In: Resolution of singularities (ed. H. Hauser at al.), 231-238, Progr. in Math. 181, Birkhäuser, Basel, 2000. MR 2001e:14001
- [BV 1]
- Bravo, A., Villamayor, O.: Strengthening the theorem of embedded desingularization. Math. Res. Lett. 8 (2001), no. 1-2, 79-89. MR 2002b:14019
- [BV 2]
- Bravo, A., Villamayor, O.: A strengthening of resolution of singularities in characteristic zero. Proc. London Math. Soc. 86 (2003), 327-357.
- [EH]
- Encinas, S., Hauser, H.: Strong resolution of singularities in characteristic zero. Comment. Math. Helv. 77 (2002), 821-845.
- [EV 1]
- Encinas, S., Villamayor, O.: Good points and constructive resolution of singularities. Acta Math. 181 (1998), 109-158. MR 99i:14020
- [EV 2]
- Encinas, S., Villamayor, O.: A course on constructive desingularization and equivariance. In: Resolution of Singularities (ed.: H. Hauser et al.), Progress in Math. 181, Birkhäuser, Basel, 2000. MR 2001g:14018
- [EV 3]
- Encinas, S., Villamayor, O.: A proof of desingularization over fields of characteristic zero. Preprint. Download at http://arXiv.org/archive/math, math.AG/0101208.
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- Grothendieck, A.: Traveaux de Heisouké Hironaka sur la résolution des singularités. Actes Congrès International Math., Nice, 1970, Gauthier-Villars, Paris, 1971. MR 54:2386
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- Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. Math. 79 (1964), 109-326. MR 33:7333
- [Hi 6]
- Hironaka, H.: Idealistic exponents of singularity. In: Algebraic Geometry, the Johns Hopkins Centennial Lectures. Johns Hopkins University Press, 1977. MR 58:16661
- [Hi 8]
- Hironaka, H.: Desingularization of complex analytic varieties. Actes Congrès International Math., Nice, 1970, Gauthier-Villars, Paris, 1971, 627-631. MR 54:13127
- [Kz]
- Kunz, E.: Algebraische Geometrie IV. Vorlesung Univ. Regensburg.
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- Lipman, J.: Introduction to resolution of singularities. Proceedings Symp. Pure Appl. Math. 29 Amer. Math. Soc., 1975, 187-230. MR 52:10730
- [M]
- Matsuki, K.: Notes on the inductive algorithm of resolution of singularities by S. Encinas and O. Villamayor. Preprint. Download at http://arXiv.org/archive/math, math.AG/0103120.
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- Villamayor, O.: Constructiveness of Hironaka's resolution. Ann. Scient. Ec. Norm. Sup. Paris 22 (1989), 1-32. MR 90b:14014
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- Villamayor, O.: Patching local uniformizations. Ann. Scient. Ec. Norm. Sup. Paris 25 (1992), 629-677.
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Additional Information
Herwig Hauser
Affiliation:
Universität Innsbruck, A-6020 Innsbruck, Austria
Email:
herwig.hauser@uibk.ac.at
DOI:
http://dx.doi.org/10.1090/S0273-0979-03-00982-0
PII:
S 0273-0979(03)00982-0
Received by editor(s):
June 25, 2002
Received by editor(s) in revised form:
December 3, 2002
Posted:
May 6, 2003
Additional Notes:
Supported in part by FWF-Project P-15551 of the Austrian Ministry of Science
Article copyright:
© Copyright 2003 American Mathematical Society
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