On the Kodaira dimension of base spaces of families of manifolds

TL;DR

This paper proves that in certain families of algebraic varieties, the variation provides a lower bound for the base's Kodaira dimension, confirming a conjecture for bases up to dimension five.

Contribution

It establishes a lower bound for the Kodaira dimension of the base in families of varieties with good minimal models, confirming a conjecture for bases of dimension five or less.

Findings

Variation bounds the Kodaira dimension of the base.

Confirms Kebekus and Kovacs' conjecture for bases up to dimension five.

Provides new insights into the structure of families of algebraic varieties.

Abstract

We prove that the variation in a smooth projective family of varieties admitting a good minimal model forms a lower bound for the Kodaira dimension of the base, if the dimension of the base is at most five and its Kodaira dimension is non-negative. This gives an affirmative answer to the conjecture of Kebekus and Kovacs for base spaces of dimension at most five.