Year: 2026
Type: preprint
Abstract: For fixed $n$ and $ε>0$, we prove boundedness of projective birational morphisms $f\colon X\to\mathbb P^n$ over $\mathbb C$ for which $(X,B)$ is an $ε$-lc pair, $B\geq 0$, $K_X+B$ is nef over $\mathbb P^n$, and $\mathrm{deg}(f_*B)$ is bounded. The nonzero coefficients of $B$ need not have a positive lower bound, and $(\mathbb P^n,f_*B)$ need not be log canonical. The $f$-exceptional prime divisors on $X$, equipped with their reduced induced scheme structures, form a bounded family of projective schemes, including when they are nonnormal. We also obtain a uniform positive lower bound for the log canonical thresholds of pullbacks of all effective target divisors of bounded degree. The boundedness statement proved in this paper was originally conjectured by Caucher Birkar.
Source: arXiv (Cornell University)
Author: Jiao, Junpeng
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7857368101
OpenAlex ID: W7220704985