Extremal higher codimension cycles of the space of complete conics

Abstract

Let $M$ denote the space of complete conics. We compute the cone of effective and numerically effective $k$-cycles of $M$, ${\mathrm{Eff}}_k(M)$ and ${\mathrm{Nef}}_k(M)$, respectively. In addition, we compute the Białynicki-Birula cell-decomposition of $M$ with respect to a ${\mathbb{C}}^{\ast }$-action and compare the cone generated by the closure of these cells to the cones ${\mathrm{Eff}}_k(M)$ and ${\mathrm{Nef}}_k(M)$.

Cited by in corpus (1)

• Higher Codimension Cycles on the Hilbert Scheme of Three Points on the Projective Plane