Toric singularities: Log-blow-ups and global resolutions
Author:
Wiesława Nizioł
Journal:
J. Algebraic Geom. 15 (2006), 1-29
DOI:
https://doi.org/10.1090/S1056-3911-05-00409-1
Published electronically:
June 27, 2005
MathSciNet review:
2177194
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References |
Additional Information
Abstract: We prove that singularities of Kato’s log-regular schemes (a base-free analogue of toroidal embeddings) can be resolved globally by a log-blow-up. This is done by showing that the classical desingularization algorithms can be globalized and extended to log-schemes.
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Ts T. Tsuji, Saturated morphisms of logarithmic schemes, preprint, 1997.
BM E. Bierstone, P. Milman,Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant, Invent. Math. 128 (1997), no. 2, 207–302.
BL S. Bosch, W. Lütkebohmert, Formal and rigid geometry. I. Rigid spaces, Math. Ann. 295 (1993), no. 2, 291–317.
Br J.-L. Brylinski, Eventails et variétés torique, Séminaire sur les singularités des surfaces, Centre de Math. de l’École Polytechnique, Palaiseau 1976-1977, Lect. Notes Math. 777, Springer-Verlag, Berlin, Heidelberg and New York, 1980, 247–288.
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D V. Danilov, The geometry of toric varieties, Russ. Math. Surveys 33 (1978), 97–154.
E2 G. Ewald, Combinatorial convexity and algebraic geometry, Graduate Texts in Mathematics, 168. Springer-Verlag, New York, 1996.
FK K. Fujiwara, K. Kato, Logarithmic étale topology theory, preprint, 1995.
Fu W. Fulton, Introduction to toric varieties, Princeton University Press, Princeton, 1993.
I L. Illusie, Logarithmic smoothness and vanishing cycles, preprint, 1996.
I1 L. Illusie, An overview of the work of K. Fujiwara, K. Kato, and C. Nakayama on logarithmic étale cohomology, Cohomologies $p$-adiques et applications arithmétiques, II. Astérisque No. 279 (2002), 271–322.
Kj T. Kajiwara, Logarithmic compactifications of the generalized Jacobian variety, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 40 (1993), no. 2, 473–502.
Ka1 K. Kato, Logarithmic structures of Fontaine-Illusie, Algebraic analysis, geometry and number theory (J. I. Igusa ed.), Johns Hopkins University Press, Baltimore, 1989, 191–224.
Ka K. Kato, Toric singularities, Amer. J. Math. 116 (1994), 1073–1099.
Ka2 K. Kato, Logarithmic degeneration and Dieudonné theory, preprint.
KK G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat, Toroidal embeddings. I. Lecture Notes in Mathematics, Vol. 339. Springer-Verlag, Berlin-New York, 1973.
O A. Ogus, Logarithmic de Rham cohomology, preprint, 1997.
Ts T. Tsuji, Saturated morphisms of logarithmic schemes, preprint, 1997.
Additional Information
Wiesława Nizioł
Affiliation:
Department of Mathematics, College of Science, University of Utah, Salt Lake City, Utah 84112-0090
Email:
niziol@math.utah.edu
Received by editor(s):
January 6, 2003
Received by editor(s) in revised form:
February 10, 2005
Published electronically:
June 27, 2005
