Vol. 11, No. 1, 2021

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The relative canonical resolution: Macaulay2-package, experiments and conjectures

Christian Bopp and Michael Hoff

Vol. 11 (2021), 15–24
DOI: 10.2140/jsag.2021.11.15
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 k + 1 and pencils of degree k for n 1, we conjecture that the syzygy divisors on the Hurwitz scheme g,k constructed by Deopurkar and Patel (Contemp. Math. 703 (2018) 209–222) all have the same support.

Keywords
Hurwitz space, syzygy modules, relative canonical resolution
Mathematical Subject Classification 2010
Primary: 13D02, 14H51, 14Q05
Supplementary material

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

Milestones
Received: 31 July 2018
Revised: 22 June 2020
Accepted: 28 August 2020
Published: 23 January 2021
Authors
Christian Bopp
Universität des Saarlandes
Saarbrücken
Germany
Michael Hoff
Universität des Saarlandes
Saarbrücken
Germany