Compactifications of affine homology 3-cells into blow-ups of the projective 3-space with trivial log canonical divisors

Abstract

We classify all the compactifications of affine homology 3-cells into the blow-ups of the projective 3-space along smooth curves such that the log canonical divisors are linearly trivial. As a result, we prove that each embedded affine 3-fold is isomorphic to the affine 3-space except one example.

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Acknowledgements

The author is greatly indebted to Professor Hiromichi Takagi, his supervisor, for his encouragement, comments, and suggestions. He wishes to express his gratitude to Professor Takashi Kishimoto for his helpful comments and suggestions. He also would like to express his gratitude to Doctor Akihiro Kanemitsu and Doctor Takeru Fukuoka for their helpful comments.

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Correspondence to Masaru Nagaoka.

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This work was supported by JSPS KAKENHI Grant Number JP19J14397 and the Program for Leading Graduate Schools, MEXT, Japan.

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Nagaoka, M. Compactifications of affine homology 3-cells into blow-ups of the projective 3-space with trivial log canonical divisors. European Journal of Mathematics (2021). https://doi.org/10.1007/s40879-021-00450-3

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Keywords

  • Affine homology threefolds
  • Compactifications
  • Blow-ups of the projective 3-space

Mathematics Subject Classification (2000)

  • 14J10
  • 14J30
  • 14M27
  • 14R10