Imaginary quadratic points on toric varieties via universal torsors

TL;DR

This paper proves Manin's conjecture for toric varieties over imaginary quadratic fields using universal torsors and lattice point counting, providing a new and elementary approach.

Contribution

It offers a novel proof of Manin's conjecture for toric varieties over imaginary quadratic fields employing universal torsors and elementary lattice counting methods.

Findings

Established the conjecture for a new class of fields

Developed an elementary counting technique

Provided a new proof approach

Abstract

Inspired by a paper of Salberger we give a new proof of Manin's conjecture for toric varieties over imaginary quadratic number fields by means of universal torsor parameterizations and elementary lattice point counting.