Abstract

This short note provides a quick introduction to relative canonical resolutions of curves on rational normal scrolls. We present our Macaulay2 package that computes the relative canonical resolution associated to a curve and a pencil of divisors. We end with a list of conjectural shapes of relative canonical resolutions. In particular, for curves of genus $g=n\cdot k+1$ and pencils of degree $k$ for $n\ge 1$, we conjecture that the syzygy divisors on the Hurwitz scheme ${\mathcal{\mathscr{H}}}_{g,k}$ constructed by Deopurkar and Patel (Contemp. Math. 703 (2018) 209–222) all have the same support.

Keywords

Mathematical Subject Classification 2010

Supplementary material

Relative canonical resolution for $g$-nodal canonical curves with a fixed $g^1_k$

Milestones

Authors