The Generalized Bloch Conjecture for the quotient of certain Calabi-Yau varieties

TL;DR

This paper proves the generalized Bloch Conjecture for certain Calabi-Yau quotient varieties, demonstrating new results on zero cycles, Lawson homology, and the Hodge Conjecture in this context.

Contribution

It establishes the generalized Bloch Conjecture for specific Calabi-Yau quotients and computes related Lawson homology, advancing understanding of algebraic cycles on these varieties.

Findings

Bloch Conjecture holds for these quotients

Computed Lawson homology for 1-cycles and codimension two cycles

Proved the (Generalized) Hodge Conjecture for these varieties

Abstract

In this paper, the generalized Bloch Conjecture on zero cycles for the quotient of certain complete intersections with trivial canonical bundle is proved to hold. As an application of Bloch-Srinivas method on the decomposition of the diagonal, we compute the rational coefficient Lawson homology for 1-cycles and codimension two cycles for these quotient varieties. The (Generalized) Hodge Conjecture is proved to hold for codimension two cycles (and hence also for 2-cycles) on these quotient varieties.