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The Rank of Syzygies of Canonical Curves

Michael Kemeny

Abstract

We prove that the linear syzygy spaces of a general canonical curve are spanned by syzygies of minimal rank.

The Rank of Syzygies of Canonical Curves

Abstract

We prove that the linear syzygy spaces of a general canonical curve are spanned by syzygies of minimal rank.

Paper Structure

This paper contains 8 sections, 36 theorems, 188 equations.

Table of Contents

  1. Introduction
  2. Rank of a Syzygy
  3. Preliminaries
  4. Notation and Background on Syzygies
  5. Rank of a Syzygy
  6. Brill--Noether Theory for Integral Curves Lying on a Surface
  7. The Projection Map
  8. The Geometric Syzygy Conjecture

Key Result

Theorem 2

Conjecture geo-conj holds for a general curve of genus $g \geq 8$.

Theorems & Definitions (78)

  • Conjecture 1: The Geometric Syzygy Conjecture
  • Theorem 2
  • Lemma 1.1
  • proof
  • Proposition 1.2: Semicontinuity of Koszul cohomology
  • proof
  • Proposition 1.3
  • proof
  • Proposition 1.4
  • proof
  • ...and 68 more