Kodaira dimension of fibrations over abelian varieties

Fanjun Meng; Mihnea Popa

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Kodaira dimension of fibrations over abelian varieties

Fanjun Meng, Mihnea Popa

Algebraic Geometry · Submitted 28 Nov 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs.

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arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs.	result 0.67	0.95	0.89	asserted 1.00

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The paper

Original abstract

We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log pairs.

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References

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5 arXiv papers cite this in 12 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

Builds on it 1 paper

It can be viewed as a generalization of [ref] to the case when $D$ is not necessarily the zero divisor.

On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture · Main theorems · 0.98

Uses its method or tool 1 paper

In the proofs of the main theorems, we employ results from [ref] , [ref] and [ref] , and arguments on positivity properties of coherent sheaves.

On surjective morphisms to abelian varieties and a generalization of the Iitaka conjecture · Main theorems · 0.96

Cites it as support 1 paper

Indeed, if we assume that $f X →A$ is smooth, a recent result of Meng-Popa [ref] shows that $κ(X) = κ(F)$.

Nowhere vanishing holomorphic one-forms and fibrations over abelian varieties · Introduction · 1.00

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