Counting imaginary quadratic points via universal torsors, II

TL;DR

This paper proves Manin's conjecture for four specific quartic del Pezzo surfaces over imaginary quadratic fields by employing the universal torsor method, advancing understanding in algebraic geometry and number theory.

Contribution

It extends the universal torsor technique to new classes of algebraic surfaces over imaginary quadratic fields, providing the first proof of Manin's conjecture in this context.

Findings

Manin's conjecture is verified for four singular quartic del Pezzo surfaces over imaginary quadratic fields.

The universal torsor method is successfully applied to these surfaces.

The results contribute to the broader understanding of rational points on algebraic varieties.

Abstract

We prove Manin's conjecture for four singular quartic del Pezzo surfaces over imaginary quadratic number fields, using the universal torsor method.