On the Effective Nonvanishing of Varieties of Kodaira Dimension Zero

TL;DR

This paper proves that for smooth projective varieties with Kodaira dimension zero, a uniform multiple of the canonical bundle has nonzero sections, depending on invariants of the Albanese fiber.

Contribution

It establishes a uniform nonvanishing result for the canonical bundle of varieties with Kodaira dimension zero based on Albanese fiber invariants.

Findings

Existence of a constant m ensuring |mK_X| is nonempty.

Dependence of m on invariants of the Albanese fiber.

Advancement in understanding the canonical bundle for Kodaira dimension zero varieties.

Abstract

Given a smooth projective variety $X$ of Kodaira dimension zero, we show that there exists a constant $m$ depending on two invariants of the general fiber of the Albanese map, such that $|mK_X|\neq\emptyset$ .