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Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties

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References

  • [A] M. Artin: On the solutions of analytic equations. Invent. Math.5, 277–291 (1968)

    Google Scholar 

  • [C] C.H. Clemens: Degenerations of Kähler manifolds. Duke Math. J.44, 215–290 (1977)

    Google Scholar 

  • [D] P. Deligne: Théorie de Hodge III. Publ. Math. IHES.44, 5–77 (1975)

    Google Scholar 

  • [F] R. Friedman: Global smoothings of varieties with normal crossings. Ann. Math.118, 75–114 (1983)

    Google Scholar 

  • [Gra] H. Grauert: Der Satz von Kuranishi für kompakte komplexe Räume. Invent. Math.25, 107–142 (1974)

    Google Scholar 

  • [Gro] A. Grothendieck: Revetement Etale et Groupe Fondamental (SGA1). Lecture Notes in Math., vol. 224, Berlin: Hodelberg New York: Springer, 1971

    Google Scholar 

  • [Kat] K. Kato: Logarithmic structures of Fontaine-Illusie. In: Algebraic Analysis Geometry and Number Theory (1988), Johns Hopkins University, pp. 191–224

  • [K] Y. Kawamata: Unobstructed deformations—a remark on a paper of Z. Ran. J. Alg. Geom.1, 183–190 (1992).

    Google Scholar 

  • [Ku] V. Kulikov: Degenerations of K3 and Enriques surfaces. Math. USSR-Izv.11, 957–989 (1977)

    Google Scholar 

  • [P] U. Persson: On Degeneration of Surfaces. Mem. AMS., vol. 189, 1977

  • [PP] U. Persson, H. Pinkham: Degeneration of surfaces with trivial canonical bundle. Ann. Math.113, 45–66 (1981)

    Google Scholar 

  • [R] Z. Ran: Deformations of manifolds with torsion or negative canonical bundle. J. Alg. Geom.1, 279–291 (1992)

    Google Scholar 

  • [Sch] M. Schlessinger: Functors of Artin rings. Trans. AMS130, 208–222 (1968)

    Google Scholar 

  • [St] J. Steebrink: Limits of Hodge structure. Invent. Math.31, 229–257 (1976)

    Google Scholar 

  • [Wa] J. Wavrick: Obstructions to the existence of a space of moduli. In: Global Analysis, papers in honor of K. Kodaira, D.C. Spencer and S. Iyanaga (eds.), Univ. Tokyo Press and Princeton University Press, 1969, pp. 403–414

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Dedicated to Professor Shoshichi Kobayashi on his sixtieth birthday

Oblatum 27-VIII-1992 & 9-X-1993

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Kawamata, Y., Namikawa, Y. Logarithmic deformations of normal crossing varieties and smoothing of degenerate Calabi-Yau varieties. Invent Math 118, 395–409 (1994). https://doi.org/10.1007/BF01231538

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