Resolutions of General Canonical Curves on Rational Normal Scrolls
Christian Bopp, Michael Hoff

TL;DR
This paper investigates the structure of the relative canonical resolution of a general canonical curve on a rational normal scroll, revealing conditions under which the bundle of quadrics becomes unbalanced based on Brill-Noether theory.
Contribution
It provides a criterion for when the bundle of quadrics in the relative canonical resolution is unbalanced, linking geometric properties to Brill-Noether numbers.
Findings
Bundle of quadrics is unbalanced if and only if a0>0 and a specific quadratic inequality holds.
The study connects the unbalanced condition to the Brill-Noether number a0.
Results apply to general curves with certain genus and gonality conditions.
Abstract
Let be a general curve of genus and let be a positive integer such that the Brill-Noether number and . The aim of this short note is to study the relative canonical resolution of on a rational normal scroll swept out by a with general. We show that the bundle of quadrics appearing in the relative canonical resolution is unbalanced if and only if and .
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