Some geometric properties of Hilbert schemes of space curves

Abstract

Let $H$ be the Hilbert scheme of curves in complex projective $3$-space, with $d\ge 3$ and genus $g\le (d-2{)}^2/4$. A complete, explicit description of the cone of curves and the ample cone of $H$ is given. From this, partial results on the group $\mathrm{Aut}(H)$ are deduced.

arXiv commentSome minor mistakes corrected; only minimal progress for Aut(H). Comments are welcome

References in corpus (1)

• On the geometry of the Hilbert schemes of points in the projective plane