Algebra Seminar 

08/07/2010, 15:00 — 16:00 — Room P4.35, Mathematics Building
Javier Elizondo, Universidad Nacional Autónoma de México

The motivic Euler-Chow series

Consider the formal power series $\sum [C_{p,\alpha (X)}]t^{\alpha }$ (called Motivic Chow Series), where $C_p(X)=\coprod C_{p,\alpha }(X)$ is the Chow variety of $X$ parametrizing the $p$- dimensional effective cycles on $X$ with $C_{p,\alpha }(X)$ its connected components, and $[C_{p,\alpha }(X)]$ its class in $K(ChM{)}_{A^1}$, the $K$-ring of Chow motives modulo $A^1$-homotopy. Using Picard product formula and Torus action, we will show that the Motivic Chow Series is rational in many cases.