Hyperelliptic limits of quadrics through canonical curves and ribbons

Abstract

We describe explicitly all hyperelliptic limits of quadrics through smooth canonical curves of genus $g$ in ${\mathbb{P}}^{g-1}$. Also, we construct an open embedding of the blow up of a ${\mathrm{PGL}}_g$-bundle over the moduli space of curves of genus $g$ along the hyperelliptic locus into the blow up of the canonical Hilbert scheme of ${\mathbb{P}}^{g-1}$ along the closure of the locus of canonical ribbons, which are certain double thickenings of rational normal curves introduced and studied by Bayer and Eisenbud.

arXiv comment31 pages