The relative canonical resolution: Macaulay2package, experiments and conjectures
Abstract
This short note provides a quick introduction to relative canonical resolutions of curves on rational normal scrolls. We present our Macaulay2package which computes the relative canonical resolution associated to a curve and a pencil of divisors. Most of our experimental data can be found on a dedicated webpage. 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 space $\mathscr{H}_{g,k}$ constructed by Deopurkar and Patel all have the same support.
 Publication:

arXiv eprints
 Pub Date:
 July 2018
 DOI:
 10.48550/arXiv.1807.05121
 arXiv:
 arXiv:1807.05121
 Bibcode:
 2018arXiv180705121B
 Keywords:

 Mathematics  Algebraic Geometry;
 14Q05;
 14H51;
 13D02
 EPrint:
 11 pages