Special Linear Series and Syzygies of Canonical Curves of Genus 9

Details Special Linear Series and Syzygies of Canonical Curves of Genus 9 Special Linear Series and Syzygies of Canonical Curves of Genus 9

2006-05-30

arxiv.org/abs/math/0605758v1

Mathematics

Algebraic Geometry

PhD Thesis, extended version

Scientific paper

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 $\operatorname{Cliff}(C)=3$ 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.

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