Special Linear Series and Syzygies of Canonical Curves of Genus 9

Abstract

In this thesis we give a complete description of the syzygies of irreducible, nonsingular, canoncial curves $C$ of genus 9. This includes a collection of all possible Betti tables for $C$. Moreover a direct correspondence between these Betti tables and the number and types of special linear series on $C$ is given. Especially for $\mathrm{Cliff}(C)=3$ the curve $C$ is contained in determinantal surface $Y$ on a 4-dimensional rational normal scroll $X\subset {\mathbb{P}}^8$ constructed from a base point free pencil of divisors of degree 5.

PhD Thesis, extended version