Desingularization of toric and binomial varieties
Authors:
Edward Bierstone and Pierre D. Milman
Journal:
J. Algebraic Geom. 15 (2006), 443-486
DOI:
https://doi.org/10.1090/S1056-3911-06-00430-9
Published electronically:
March 1, 2006
MathSciNet review:
2219845
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Abstract |
References |
Additional Information
Abstract: We give a combinatorial algorithm for equivariant embedded resolution of singularities of a toric variety defined over a perfect field. The algorithm is realized by a finite succession of blowings-up with smooth invariant centres that satisfy the normal flatness condition of Hironaka. The results extend to more general varieties defined locally by binomial equations.
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[Be]Be B.M. Bennett, On the characteristic function of a local ring, Ann. of Math. (2) 91 (1970), 25–87.
[BM1]BMihes E. Bierstone and P.D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5–42.
[BM2]BMjams E. Bierstone and P.D. Milman, Uniformization of analytic spaces, J. Amer. Math. Soc. 2 (1989), 801–836.
[BM3]BMinv E. Bierstone and P.D. Milman, Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128 (1997), 207–302.
[BM4]BMsam E. Bierstone and P.D. Milman, Standard basis along a Samuel stratum and implicit differentiation, The Arnoldfest, Proceedings of a Conference in Honour of V.I. Arnold for his Sixtieth Birthday, ed. E. Bierstone, B. Khesin, A. Khovanskii and J. Marsden, Fields Inst. Comm., vol. 24, Amer. Math. Soc., Providence, 1999, pp. 81–113.
[BM5]BMda1 E. Bierstone and P.D. Milman, Desingularization algorithms I. Role of exceptional divisors, Moscow Math. J. 3 (2003), 751–805.
[C]Cox D.A. Cox, Toric varieties and toric resolution, Resolution of Singularities, A Research Textbook in Tribute to Oscar Zariski, Progress in Math., vol. 181, Birkhäuser, Basel, Boston, Berlin, 2000, pp. 259–284.
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[ES]ES D. Eisenbud and B. Sturmfels, Binomial ideals, Duke Math. J. 84 (1996), 1–45.
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[ZS]ZS O. Zariski and P. Samuel, Commutative Algebra Vol. I, Van Nostrand, Princeton, 1958.
Additional Information
Edward Bierstone
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
Email:
bierston@math.toronto.edu
Pierre D. Milman
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
Email:
milman@math.toronto.edu
Received by editor(s):
December 3, 2004
Received by editor(s) in revised form:
September 15, 2005
Published electronically:
March 1, 2006
Additional Notes:
The authors’ research was supported in part by NSERC grants OGP0009070 and OGP0008949
