Murre's conjectures and explicit Chow--Kuenneth projectors for some varieties

TL;DR

This paper constructs explicit Chow--Künneth projectors for certain varieties with nef tangent bundles, verifying Murre's conjectures and the motivic Hard Lefschetz theorem for these cases.

Contribution

It provides explicit Chow--Künneth projectors for varieties with nef tangent bundles, confirming Murre's conjectures and the motivic Hard Lefschetz theorem.

Findings

Explicit projectors for nef tangent bundle varieties

Verification of Murre's conjectures in these cases

Confirmation of the motivic Hard Lefschetz theorem

Abstract

In this paper, we investigate Murre's conjectures on the structure of rational Chow groups and exhibit explicit Chow--Kuenneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle explicit Chow--Kuenneth projectors are obtained which satisfy Murre's conjectures and the motivic Hard Lefschetz theorem is verified.