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 Cliff(C) = 3 the curve C is contained in determinantal surface Y on a 4-dimensional rational normal scroll Xsubsetmathbb{P}^{8} constructed from a base point free pencil of divisors of degree 5.