Nef and effective cones of the Hilbert scheme of 3 points in \(\mathbb{P}^3\)

Gwyneth Moreland, Harvard University

We compute some higher (co)dimension nef and effective cones of the Hilbert scheme of 3 points in \(\mathbb{P}^3\). This involves studying the orbits of the PGL action on the Hilbert scheme, as well as extending Mallavibarrena and Sols' bases for the Chow groups of Hilbert schemes of points on \(\mathbb{P}^2\) to the case of the Hilbert scheme of 3 points in \(\mathbb{P}^3\). This work builds on results of Ryan and Stathis.

MC 5417