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Del Pezzo surfaces of degree 1 and jacobians

Yuri G. Zarhin

Abstract

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.

Del Pezzo surfaces of degree 1 and jacobians

Abstract

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.

Paper Structure

This paper contains 5 sections, 23 theorems, 117 equations.

Table of Contents

  1. Introduction
  2. Del Pezzo surfaces of degree $1$
  3. Abelian varieties
  4. Jacobians
  5. Explicit formulas

Key Result

Theorem 1.1

Let $f(t)\in K[t]$ be an irreducible degree $8$ polynomial, whose Galois group is either ${\mathbf S}_8$ or $\mathbf{A}_8$. Let ${\mathfrak R}\subset K_a$ be the set of roots of $f$. Then:

Theorems & Definitions (54)

  • Theorem 1.1
  • Example 1.2
  • Example 1.3
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • Remark 2.5
  • Remark 2.6
  • Lemma 2.7
  • ...and 44 more