K-trivial structures on Fano complete intersections

TL;DR

This paper proves that for generic Fano complete intersections of certain dimensions, any fiber space structure with Kodaira dimension zero is essentially a pencil of hyperplanes, and describes K-trivial structures on related varieties.

Contribution

It establishes the uniqueness of K-trivial fiber structures on generic Fano complete intersections of index one under specific dimension conditions.

Findings

Any fiber space with Kodaira dimension zero is a pencil of hyperplanes.

K-trivial structures on certain varieties are classified.

Results apply to Fano complete intersections with dimension constraints.

Abstract

It is proven that any structure of a fibre space into varieties of Kodaira dimension zero on a generic Fano complete intersection of index one and dimension $M$ in ${\mathbb P}^{M+k}$ for $M\geq 2k+1$ is a pencil of hyperplane sections. We also describe $K$-trivial structures on varieties with a pencil of Fano complete intersections.