Hilbert schemes of fat r-planes and triviality of Chow groups of complete intersections

TL;DR

This paper explores the triviality of rational Chow groups of complete intersections in projective spaces, providing improved bounds and analyzing Hilbert schemes of fat r-planes to generalize known results about Fano varieties.

Contribution

It introduces new bounds for Chow group triviality and extends the understanding of Hilbert schemes of fat r-planes in complete intersections.

Findings

Improved bounds for Chow group triviality.

Dimension and nonemptiness results for Hilbert schemes of fat r-planes.

Generalization of results on Fano varieties of r-planes.

Abstract

In this paper, we investigate the question of triviality of the rational Chow groups of complete intersections in projective spaces and obtain improved bounds for this triviality to hold. Along the way, we study the dimension and nonemptiness of some Hilbert schemes of fat $r$-planes contained in a complete intersection $Y$, generalizing well-known results on the Fano varieties of $r$-planes contained in $Y$.