On irregular threefolds of Kodaira dimension two

Let $X$ be an irregular threefold of Kodaira dimension two. We show that the Iitaka volume $\operatorname{Ivol}(X)$ of $X$ is at least $\frac{1}{100}$ and $\lvert mK_X\rvert$ defines the Iitaka fibration for $m\geq 32$. Both $\frac{1}{100}$ and $32$ are sharp.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-26
DOI
https://doi.org/10.48550/arxiv.2610.34955
Primary Topic
Algebraic Geometry and Number Theory
Type
preprint
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preprint

On irregular threefolds of Kodaira dimension two

Ziqi Liu, Pengjin Wang
arXiv (Cornell University)
Algebraic Geometry and Number Theory
preprint

On irregular threefolds of Kodaira dimension two

Ziqi Liu, Pengjin Wang
preprint en

Abstract

Let $X$ be an irregular threefold of Kodaira dimension two. We show that the Iitaka volume $\operatorname{Ivol}(X)$ of $X$ is at least $\frac{1}{100}$ and $\lvert mK_X\rvert$ defines the Iitaka fibration for $m\geq 32$. Both $\frac{1}{100}$ and $32$ are sharp.

arXiv (Cornell University)
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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On irregular threefolds of Kodaira dimension two — Ziqi Liu, Pengjin Wang · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS