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Points of bounded height on quintic del Pezzo surfaces over the rational numbers

Christian Bernert, Ulrich Derenthal

Abstract

We give a relatively short and elementary proof of Manin's conjecture for split smooth quintic del Pezzo surfaces over the rational numbers.

Points of bounded height on quintic del Pezzo surfaces over the rational numbers

Abstract

We give a relatively short and elementary proof of Manin's conjecture for split smooth quintic del Pezzo surfaces over the rational numbers.
Paper Structure (15 sections, 19 theorems, 94 equations)

This paper contains 15 sections, 19 theorems, 94 equations.

Table of Contents

  1. Introduction
  2. Parameterization and symmetry
  3. Universal torsor parameterization
  4. Symmetry
  5. Dependent coordinates
  6. Restrictions of the counting problem
  7. Restricting the $a_{ij}$
  8. Restricting the $a_i$
  9. Removing the symmetry condition
  10. Estimation of the main contribution
  11. Möbius inversion
  12. Large Möbius variables
  13. Lattice point counting
  14. The local densities
  15. Completion of the proof

Key Result

Theorem 1

We have for $B \ge 3$, where with $\alpha(X)=\frac{1}{144}$ and

Theorems & Definitions (39)

  • Theorem
  • Proposition 2.1
  • proof
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Proposition 3.1
  • proof
  • Lemma 3.2
  • ...and 29 more