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arXiv · 1711.04535

On an open problem of characterizing the birationality of 4K

Meng Chen·Yong Hu
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Abstract

We answer an open problem raised by Chen and Zhang in 2008 and prove that, for any minimal projective 3-fold $X$ of general type with the geometric genus $\geq 5$, $X$ is birationally fibred by a pencil of $(1,2)$-surfaces (i.e. $c_1^2=1$, $p_g=2$) if and only if the $4$-canonical map $\varphi_{4,X}$ is non-birational. The statement does not hold for those with the geometric genus $\leq 4$ according to our examples.

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Meng Chen, Yong Hu. 2017-11-13. On an open problem of characterizing the birationality of 4K. https://arxiv.org/abs/1711.04535

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