On an open problem of characterizing the birationality of \(\mathrm{4K}\)

DOI10.4310/CAG.2021.V29.N7.A2zbMATH Open1487.14084arXiv1711.04535OpenAlexW2808147056MaRDI QIDQ2141008

Yanyan Li

Publication date: 23 May 2022

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

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 $geq5$, $X$ 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 $varph{i}_{4,X}$ is non-birational. The statement does not hold for those with the geometric genus $leq4$ according to our examples.

Full work available at URL: https://arxiv.org/abs/1711.04535

zbMATH Keywords

geometric genus

Mathematics Subject Classification ID

(3)-folds (14J30) Rational and birational maps (14E05)

Related Items (1)

Birational positivity in dimension 4

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