On Manin's conjecture for a certain singular cubic surface over imaginary quadratic fields

TL;DR

This paper proves Manin's conjecture for a specific singular cubic surface over imaginary quadratic fields, advancing understanding of rational points on algebraic varieties in number theory.

Contribution

It establishes Manin's conjecture for a cubic surface with an E_6 singularity over imaginary quadratic fields, a case previously unverified.

Findings

Confirmed Manin's conjecture for the specified surface.

Demonstrated techniques applicable to similar singular surfaces.

Extended the scope of Manin's conjecture to new algebraic cases.

Abstract

We prove Manin's conjecture over imaginary quadratic number fields for a cubic surface with a singularity of type E_6.