Manin conjecture

In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function.

It was proposed by Yuri I. Manin and his collaborators[1] in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties.

be a Fano variety defined over a number field

be a height function which is relative to the anticanonical divisor and assume that

Then there exists a non-empty Zariski open subset

is a positive constant which later received a conjectural interpretation by Peyre.

[2] Manin's conjecture has been decided for special families of varieties,[3] but is still open in general.