Prelog Chow groups of self-products of degenerations of cubic threefolds

TL;DR

This paper investigates the algebraic cycles of degenerations of cubic threefolds by computing their prelog Chow groups, aiming to understand their rationality and Chow-theoretic properties.

Contribution

It introduces the computation of the saturated numerical prelog Chow group for a specific degeneration of cubic threefolds, advancing the study of their algebraic and rationality properties.

Findings

Computed the prelog Chow group for a degeneration of cubic threefolds

Provided new insights into the Chow-theoretic structure of degenerations

Laid groundwork for future rationality and decomposition of the diagonal studies

Abstract

It is unknown whether smooth cubic threefolds have an (integral Chow-theoretic) decomposition of the diagonal, or whether they are stably rational or not in general. As a first step towards making progress on these questions, we compute the (saturated numerical) prelog Chow group of the self-product of a certain degeneration of cubic threefolds.