De-Yuan Ma

Poincar\'e series of degree-two Chow varieties

Let $C_{p, 2}(\mathbb{P}^{n})$ denote the Chow variety parametrizing effective algebraic $p$-cycles of degree two on $\mathbb{P}^{n}$. We show that its rational cohomology is pure Tate and concentrated in even degrees. An anti-invariant Chern class identity yields a presentation of the cohomology ring as a fiber produc...