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On Ueno’s conjecture K

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Abstract

We show that if X is a smooth complex projective variety with Kodaira dimension 0 then the Kodaira dimension of a general fiber of its Albanese map is at most \({h^0(\Omega ^1 _X)}\) .

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd, Taipei, 10617, Taiwan

    Jungkai A. Chen

  2. Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, UT, 84112-0090, USA

    Christopher D. Hacon

Authors
  1. Jungkai A. Chen
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  2. Christopher D. Hacon
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Correspondence to Jungkai A. Chen.

Additional information

J. A. Chen was partially supported by NCTS, TIMS, and NSC of Taiwan. C. D. Hacon was partially supported by NSF research grant no: 0456363 and an AMS Centennial Scholarship. We would like to thank J. Kollár, R. Lazarsfeld, C.-H. Liu, M. Popa, P. Roberts, and A. Singh for many useful comments on the contents of this paper.

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Chen, J.A., Hacon, C.D. On Ueno’s conjecture K. Math. Ann. 345, 287–296 (2009). https://doi.org/10.1007/s00208-009-0352-6

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  • DOI: https://doi.org/10.1007/s00208-009-0352-6

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