Resolutions of General Canonical Curves on Rational Normal Scrolls

Abstract

Let $C\subset {\mathbb{P}}^{g-1}$ be a general curve of genus $g$ and let $k$ be a positive integer such that the Brill-Noether number $\rho (g,k,1)\ge 0$ and $g>k+1$. The aim of this short note is to study the relative canonical resolution of $C$ on a rational normal scroll swept out by a $g_k^1=|L|$ with $L\in W_k^1(C)$ general. We show that the bundle of quadrics appearing in the relative canonical resolution is unbalanced if and only if $\rho >0$ and $(k-\rho -\frac{7}{2}{)}^2-2k+\frac{23}{4}>0$.

11 pages, 1 figure

Cited by in corpus (2)

• A characterization of bielliptic curves via syzygy schemes
• The relative canonical resolution: Macaulay2-package, experiments and conjectures