Tohoku Mathematical Journal

Log smooth deformation theory

Fumiharu Kato

Full-text: Open access

Article information

Source
Tohoku Math. J. (2) Volume 48, Number 3 (1996), 317-354.

Dates
First available: 3 May 2007

Permanent link to this document
http://projecteuclid.org/euclid.tmj/1178225336

Mathematical Reviews number (MathSciNet)
MR1404507

Zentralblatt MATH identifier
0876.14007

Digital Object Identifier
doi:10.2748/tmj/1178225336

Subjects
Primary: 14D15: Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]

Citation

Kato, Fumiharu. Log smooth deformation theory. Tohoku Mathematical Journal 48 (1996), no. 3, 317--354. doi:10.2748/tmj/1178225336. http://projecteuclid.org/euclid.tmj/1178225336.


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References

  • [1] R. FRIEDMAN, Global smoothings of varieties with normal crossings, Ann. of Math. (2) 118 (1983), 75-114.
  • [2] A. GROTHENDIECK, Revetements etales et groupe fondamentale, Lecture Notes in Math. 224, Springer-Verlag, Berlin, 1971.
  • [3] L. ILLUSIE, Introduction a la geometric logarithmique, Seminar notes at Univ. of Tokyo in 1992
  • [4] T. KAJIWARA, Logarithmic compactifications of the generalized Jacobian variety, J. Fac. Sci. Univ Tokyo, Sect. IA, Math. 40 (1993), 473-502.
  • [5] K. KATO, Logarithmic structures of Fontaine-IIIusie, in Algebraic Analysis, Geometry and Numbe Theory (J. -I. Igusa, ed.), Johns Hopkins Univ., 1988, 191-224.
  • [6] Y. KAWAMATA AND Y. NAMIKAWA, Logarithmic deformations of normal crossing varieties an smoothings of degenerate Calabi-Yau varieties, Invent. Math. 118 (1994), 395^09.
  • [7] K. KODAIRA AND D. C. SPENCER, On deformation of complex analytic structures, I-II, Ann. of Math (2) 67 (1958), 328-466.
  • [8] S. LICHTENBAUM AND M. ScHLESSiNGER, The cotangent complex of a morphism, Trans. Amer. Math Soc. 128 (1967), 41-70.
  • [9] K. MAKIO, On the relative pseudo-rigidity, Proc. Japan Acad. Sect. IA 49 (1973), 6-9
  • [10] T. ODA, Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties, Ergebnisse der Math. (3) 15, Springer-Verlag, Berlin-New York, 1988.
  • [11] M. SCHLESSINGER, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222
  • [12] J. H. M. STEENBRINK, Logarithmic embeddings of varieties with normal crossings and mixed Hodg structures, Math. Ann. 301 (1995), 105-118.