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Pencils on general covers of an elliptic curve

Andreas Leopold Knutsen, Margherita Lelli-Chiesa

Abstract

We completely describe the Brill-Noether theory of pencils on general primitive covers of elliptic curves of any degree.

Pencils on general covers of an elliptic curve

Abstract

We completely describe the Brill-Noether theory of pencils on general primitive covers of elliptic curves of any degree.
Paper Structure (2 sections, 8 theorems, 23 equations)

This paper contains 2 sections, 8 theorems, 23 equations.

Table of Contents

  1. Introduction
  2. Proofs of the results

Key Result

Theorem 1

Let $\varphi:C\to E$ define a general point in the Hurwitz scheme ${\mathcal{H}}^{\tiny \hbox{prim}}_{g,k}(E)$ for $g\geqslant 2$ and $k\geqslant 2$. Let $G^1_d(C)^{nc}$ denote the closure of the locus of linear series in $G^1_d(C)$ that are base point free and not composed with $\varphi$. Then the

Theorems & Definitions (15)

  • Theorem 1
  • Corollary 2
  • Corollary 3
  • Proposition 4
  • proof
  • Proposition 5
  • proof
  • Lemma 6
  • proof
  • Lemma 7
  • ...and 5 more