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Original Articles

Kodaira Type Vanishing Theorem for the Hirokado Variety

Pages 4744-4750 | Received 18 May 2012, Published online: 23 May 2014

REFERENCES

  • Schoen , C. ( 2009 ). Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number . Compos. Math. 145 ( 1 ): 89 – 111 .
  • Cynk , S. , Schütt , M. ( 2012 ). Non-liftable Calabi-Yau spaces . Ark. Mat. 50 ( 1 ): 23 – 40 .
  • Cynk , S. , van Straten , D. , ( 2009 ). Small resolutions and non-liftable Calabi-Yau threefolds . Manuscripta Math. 130 ( 2 ): 233 – 249 .
  • Beltrametti , M. C. , Carletti , E. , Gallarati , D. , Bragadin , G. M. ( 2009 ). Lectures on Curves, Surfaces and Projective Varieties, A Classical View of Algebraic Geometry. Textbook in Mathematics. European Mathematical Society .
  • Deligne , P. ( 1973 ). Cohomologie des intersections complètes, Groupes de monodromie én géométrie algébrique. II (Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II), SLN. no. 340, Berlin: Springer-Verlag, pp. 39–61 .
  • Deligne , P. , Illusie, Luc , L. ( 1987 ). Relèvements modulo p et décomposition du complexe de de Rham . Invent. Math. 89 ( 2 ): 247 – 270 .
  • Ekedahl , T. ( 1987 ). Foliations and inseparable morphisms. Algebraic geometry. Bowdoin, 1985 (Brunswick, Maine, 1985), 139–149, Proc. Sympos. Pure Math., 46, Part 2, Amer. Math. Soc., Providence, RI .
  • Ekedahl , T. ( 1988 ). Canonical models of surfaces of general type in positive characteristic . Inst. Hautes Etudes Sci. Publ. Math. No. 67 : 97 – 144 .
  • Ekedahl , T. On non-liftable Calabi-Yau threefolds. (Preprint). math.AG/0306435
  • Hirokado , M. ( 1999 ). A non-liftable Calabi-Yau threefold in characteristic 3. Tohoku Math. J. (2) 51(4):479–487 .
  • Hirokado , M. , Ito , H. , Saito , N. ( 2007 ). Calabi-Yau threefolds arising from fiber products of rational quasi-elliptic surfaces I . Ark. Mat. 45 ( 2 ): 279 – 296 .
  • Hirokado , M. , Ito , H. , Saito , N. ( 2008 ). Calabi-Yau threefolds arising from fiber products of rational quasi-elliptic surfaces II . Manuscripta Math. 125 ( 3 ): 325 – 343 .
  • Mukai , S. ( 2013 ). Counterexamples of Kodaira's vanishing and Yau's inequality in characteristics . Kyoto J. Math. 53 : 515 – 532 .
  • Schröer , S. (2004). Some Calabi-Yau threefolds with obstructed deformations over the Witt vectors. Compos. Math. 140(6):1579–1592.
  • Takayama , Y. ( 2012 ). Raynaud-Mukai construction and Calabi-Yau threefolds in positive characteristic . Proc. Amer. Math. Soc. 140 : 4063 – 4074 .
  • Takeda , Y. ( 2007 ). Pre-Tango structures and uniruled varieties . Colloq. Math. 108 ( 2 ): 193 – 216 .
  • Tango , H. ( 1972 ). On the behavior of extensions of vector bundles under the Frobenius map . Nagoya Math. J. 48 : 73 – 89 .
  • Raynaud , M. ( 1978 ). Contre-exemple au “vanishing theorem” en caractéristique p > 0. (French) C. P. Ramanujam—a tribute, pp. 273–278, Tata Inst. Fund. Res. Studies in Math., 8, Springer, Berlin-New York .
  • Communicated by L. Ein.

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