Absolute Chow-Kuenneth decomposition for rational homogeneous bundles and for log homogeneous varieties

TL;DR

This paper proves the existence of Chow-Kuenneth decompositions for certain rational homogeneous bundles and log homogeneous varieties, advancing Murre's conjecture in these contexts.

Contribution

It establishes Chow-Kuenneth decompositions for rational homogeneous bundles over varieties with such decompositions and for specific log homogeneous varieties, extending Murre's conjecture.

Findings

Chow-Kuenneth decomposition exists for rational homogeneous bundles over suitable bases.

The decomposition also applies to a class of log homogeneous varieties.

Results support Murre's conjecture in new geometric settings.

Abstract

In this paper, we investigate Murre's conjecture on the existence of a Chow--Kuenneth decomposition for a rational homogeneous bundle $Z\to S$ over a smooth variety, defined over complex numbers. Chow-K\"unneth decomposition is exhibited for $Z$ whenever $S$ has a Chow--Kuenneth decomposition. The same conclusion holds for a class of log homogeneous varieties, studied by M. Brion.