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On birational geometry of minimal threefolds with numerically trivial canonical divisors

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For a minimal threefold X with \(K_X\equiv 0\) and a nef and big Weil divisor L on X, we investigate the birational geometry inspired by L. We prove that |mL| and \(|K_X+mL|\) give birational maps for all \(m\ge 17\). The result remains true under weaker assumption that L is big and has no stable base components.

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Acknowledgments

The author would like to express his gratitude to his supervisor Professor Yujiro Kawamata for suggestions and encouragement. He appreciates the very effective discussion with Professors Meng Chen and Keiji Oguiso during the preparation of this paper. Part of this paper was written during the author’s visit to Fudan University and he would like to thank for the hospitality and support. The author would like to thank the anonymous reviewer for his valuable comments and suggestions to improve the explanation of the paper.

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  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Chen Jiang

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  1. Chen Jiang
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Correspondence to Chen Jiang.

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C. Jiang is supported by Grant-in-Aid for JSPS Fellows (KAKENHI No. 25-6549) and Program for Leading Graduate Schools, MEXT, Japan.

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Jiang, C. On birational geometry of minimal threefolds with numerically trivial canonical divisors. Math. Ann. 365, 49–76 (2016). https://doi.org/10.1007/s00208-015-1268-y

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  • DOI: https://doi.org/10.1007/s00208-015-1268-y

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