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The relative log Poincaré lemma and relative log de Rham theory

Fumiharu Kato
Source: Duke Math. J. Volume 93, Number 1 (1998), 179-206.
First Page: Show Hide
Primary Subjects: 32C35
Secondary Subjects: 14F40, 32J25
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077230641
Mathematical Reviews number (MathSciNet): MR1620096
Zentralblatt MATH identifier: 0947.32003
Digital Object Identifier: doi:10.1215/S0012-7094-98-09307-3

References

[1] P. Deligne, Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin, 1970.
Mathematical Reviews (MathSciNet): MR54:5232
Zentralblatt MATH: 0244.14004
[2] T. Fujisawa, Limits of Hodge structures in several variables, preprint, 1996.
Mathematical Reviews (MathSciNet): MR1668986
Zentralblatt MATH: 0940.14007
Digital Object Identifier: doi:10.1023/A:1000642525573
[3] L. Illusie, Logarithmic spaces (according to K. Kato), Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Perspect. Math., vol. 15, Academic Press, San Diego, 1994, pp. 183–203.
Mathematical Reviews (MathSciNet): MR95j:14023
Zentralblatt MATH: 0832.14015
[4] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer-Verlag, Berlin, 1994.
Mathematical Reviews (MathSciNet): MR95g:58222
Zentralblatt MATH: 0709.18001
[5] F. Kato, Log smooth deformation and moduli of log smooth curves, ms. Forschergruppe Automorphe Formen, 1996, Universität Mannheim u. Universität Heidelberg.
[6] F. Kato, Log smooth deformation theory, Tohoku Math. J. (2) 48 (1996), no. 3, 317–354.
Mathematical Reviews (MathSciNet): MR99a:14012
Zentralblatt MATH: 0876.14007
Digital Object Identifier: doi:10.2748/tmj/1178225336
Project Euclid: euclid.tmj/1178225336
[7] K. Kato, Logarithmic structures of Fontaine-Illusie, Algebraic Analysis, Geometry, and Number Theory (Baltimore, Md., 1988), Johns Hopkins Univ. Press, Baltimore, 1989, pp. 191–224.
Mathematical Reviews (MathSciNet): MR99b:14020
Zentralblatt MATH: 0776.14004
[8] K. Kato, Problems concerning log Hodge structures, preprint, 1995.
[9] K. Kato and C. Nakayama, Log Betti cohomology, log etale cohomology, and log de Rham cohomology of log schemes over $\mathbfC$, to appear in Kodai Math. J.
Mathematical Reviews (MathSciNet): MR1700591
Digital Object Identifier: doi:10.2996/kmj/1138044041
Project Euclid: euclid.kmj/1138044041
[10] Y. Kawamata and Y. Namikawa, Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties, Invent. Math. 118 (1994), no. 3, 395–409.
Mathematical Reviews (MathSciNet): MR95j:32030
Zentralblatt MATH: 0848.14004
Digital Object Identifier: doi:10.1007/BF01231538
[11] T. Matsubara, On log Hodge structures of higher direct images, Tokyo Institute of Technology, 1996.
[12] C. Nakayama, Logarithmic étale cohomology, Math. Ann. 308 (1997), no. 3, 365–404.
Mathematical Reviews (MathSciNet): MR98j:14022
Zentralblatt MATH: 0877.14016
Digital Object Identifier: doi:10.1007/s002080050081
[13] C. Nakayama, Nearby cycles for log smooth families, preprint, UTMS 94-70, University of Tokyo, 1994.
Mathematical Reviews (MathSciNet): MR1622751
Zentralblatt MATH: 0926.14006
Digital Object Identifier: doi:10.1023/A:1000327225021
[14] T. Oda, Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties, Ergeb. Math. Grenzgeb. (3), vol. 15, Springer-Verlag, Berlin, 1988.
Mathematical Reviews (MathSciNet): MR88m:14038
Zentralblatt MATH: 0628.52002
[15] T. Oda, Torus Embeddings and Applications, Tata Inst. Fund. Res. Lectures on Math. and Phys., vol. 57, Springer-Verlag, Berlin, 1978.
Mathematical Reviews (MathSciNet): MR81e:14001
Zentralblatt MATH: 0417.14043
[16] U. Persson, On degenerations of algebraic surfaces, Mem. Amer. Math. Soc. 11 (1977), no. 189, xv+144.
Mathematical Reviews (MathSciNet): MR57:6030
Zentralblatt MATH: 0368.14008
[17] J. H. M. Steenbrink, Limits of Hodge structures, Invent. Math. 31 (1975/76), no. 3, 229–257.
Mathematical Reviews (MathSciNet): MR55:2894
Zentralblatt MATH: 0303.14002
Digital Object Identifier: doi:10.1007/BF01403146
[18] J. H. M. Steenbrink, Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures, Math. Ann. 301 (1995), no. 1, 105–118.
Mathematical Reviews (MathSciNet): MR96e:14009
Zentralblatt MATH: 0814.14010
Digital Object Identifier: doi:10.1007/BF01446621
[19] S. Usui, Recovery of vanishing cycles by log geometry, preprint, 1996.
Mathematical Reviews (MathSciNet): MR1808639
Digital Object Identifier: doi:10.2748/tmj/1178207529
Project Euclid: euclid.tmj/1178207529
[20] S. Usui, Recovery of vanishing cycles by log geometry: Case of several variables, to appear in Proc. of Commutative Algebra and Algebraic Geometry (Hanoi, 1996), Lect. Notes in Math.
Mathematical Reviews (MathSciNet): MR1714854
Zentralblatt MATH: 1015.14006
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