On Fujita invariants of subvarieties of a uniruled variety

Abstract

We show that if $X$ is a smooth uniruled projective variety and $L$ a big and semiample $\mathbb{Q}$-divisor on $X$, then there exists a proper closed subset $W\subset X$ such that every subvariety $Y$ satisfying $a(Y,L)>a(X,L)$ is contained in $W$.

6 pages. Comments are welcome; v2: 7 pages, proof rewritten

Cited by in corpus (4)

• Geometric Manin's Conjecture and rational curves
• On the geometry of thin exceptional sets in Manin's Conjecture
• Manin's Conjecture and the Fujita invariant of finite covers
• On upper bounds of Manin type