Manin's b-constant in families

TL;DR

This paper proves that the b-constant, relevant to Manin's conjecture, remains constant on very general fibers of a family of algebraic varieties, with specific results for uniruled fibers.

Contribution

It establishes the constancy of the b-constant in families of algebraic varieties, extending understanding of Manin's conjecture in algebraic geometry.

Findings

b-constant is constant on very general fibers

b-constant is constant on general fibers if fibers are uniruled

advances understanding of Manin's conjecture in families

Abstract

We show that the $b$-constant (appearing in Manin's conjecture) is constant on very general fibers of a family of algebraic varieties. If the fibers of the family are uniruled, then we show that the $b$-constant is constant on general fibers.