Rationality of Motivic Chow series modulo A1-homotopy

摘要

Consider the formal power series ∑[C _(p,α)(X)]t ~α (called the Motivic Chow series), where C _p(X)={amalgamation}C _(p,α)(X) is the Chow variety of X parametrizing the p-dimensional effective cycles on X with C _(p,α)(X) its connected components, and [C _(p,α)(X)] its class in K(ChM)A1, the K-ring of Chow motives modulo A1 homotopy. Using the Picard product formula and torus action, we will show that the Motivic Chow series is rational in many cases.