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arXiv · 1309.4327

Unboundedness of fiber invariants of canonically fibred varieties of general type

Meng Chen·Zhi Jiang
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Abstract

We answer an open question concerning the boundedness of canonical fiber spaces in high dimensions and prove the following: for any set of integers $n\geq 3$, $0 0$, there exists a nonsingular projective $n$-fold $X$ of general type so that $X$ is canonically fibred by $d$-dimensional varieties $F$ with $p_g(F)\geq N$. This disproves the desired boundedness parallel to Beauville's boundedness theorem in the surface case.

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Meng Chen, Zhi Jiang. 2014-07-23. Unboundedness of fiber invariants of canonically fibred varieties of general type. https://doi.org/10.1112/blms%2Fbdu072

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