Manin's Conjecture and the Fujita invariant of finite covers

TL;DR

This paper proves a conjecture relating the Fujita invariant's behavior under finite covers, providing insights into the geometric aspects of Manin's conjecture in algebraic geometry.

Contribution

It establishes the behavior of the Fujita invariant under pull-back to finite covers, confirming a conjecture and enhancing understanding of Manin's conjecture.

Findings

Proved Lehmann-Tanimoto's conjecture on Fujita invariant behavior.

Derived results on the geometric consistency of Manin's conjecture.

Enhanced understanding of invariants under finite covers.

Abstract

We prove a conjecture of Lehmann-Tanimoto about the behaviour of the Fujita invariant (or $a$-constant appearing in Manin's conjecture) under pull-back to generically finite covers. As a consequence we obtain results about geometric consistency of Manin's conjecture.