Manin's conjecture for quartic del Pezzo surfaces with a conic fibration

TL;DR

This paper proves an asymptotic formula for counting rational points of bounded height on a specific class of quartic del Pezzo surfaces with a conic fibration, advancing understanding in algebraic geometry and number theory.

Contribution

It establishes the first asymptotic count for rational points on these surfaces, confirming Manin's conjecture in this setting.

Findings

Asymptotic formula for rational points established

Supports Manin's conjecture for these surfaces

Advances understanding of rational points on algebraic surfaces

Abstract

An asymptotic formula is established for the number of rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.