Counting rational points over number fields on a singular cubic surface

Abstract

A conjecture of Manin predicts the distribution of K-rational points on certain algebraic varieties defined over a number field K. In recent years, a method using universal torsors has been successfully applied to several hard special cases of Manin’s conjecture over the field Q. Combining this method with techniques developed by Schanuel, we give a proof of Manin’s conjecture over arbitrary number fields for the singular cubic surface S given by the equation x0 = x1x2x3.

Locations

• Algebra & Number Theory - View - PDF
• arXiv (Cornell University) - View - PDF
• Project Euclid (Cornell University) - View - PDF