Shokurov's bounded klt complements conjecture for Fano type contractions with finite rational coefficients

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Lean statement (supporting result only): CartierChartCompactnessSupport evidence for this event

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Companion manuscript: Uniform Cartier sections for Fano type contractions evidence for this event

Theorem 1.1: for every $d$ and rational $\epsilon>0$ there is $N(d,\epsilon)$ such that every projective contraction $f:X\to Z$ over an algebraically closed field of characteristic zero with $X$ $\epsilon$-lc of dimension $d$, $K_X$ $\mathbb Q$-Cartier and $-K_X$ ample over $Z$ has, near each closed point of $Z$, a boundary $B$ with $(X,B)$ klt and $N(K_X+B)\sim0$. Corollary 1.2 (over $\mathbb C$): the finite-rational-coefficient form for Fano type pairs with nef anti-log-canonical divisor, with monotone complements. The companion proves that some Cartier divisor through any base point has pulled-back lc threshold at least $\tau(d,\epsilon)$, also for real boundaries over $\mathbb C$. Not shown: $\epsilon'$-lc complements, DCC coefficient sets, or effective values of $N$. parent of this event

Shokurov's bounded klt complements conjecture for Fano type contractions with finite rational coefficients parent of this event

B. Chen, Boundedness of klt complements on Fano fibrations over surfaces (arXiv 2403.01154) evidence for this event

VibeMathed record: Shokurov's bounded klt complements conjecture for Fano type contractions with finite rational coefficients evidence for this event

Shokurov's bounded klt complements conjecture for Fano type contractions with finite rational coefficients evidence for this event