References & Citations
Mathematics > Algebraic Geometry
Title: Boundedness of klt complements on Fano fibrations over surfaces
(Submitted on 2 Mar 2024 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: Let $(X,B)$ be an $\epsilon$-lc pair of dimension $d$ with a closed point $x\in X$. Birkar conjectured that there is an effective Cartier divisor $H$ passing through $x$ such that $(X,B+tH)$ is lc near $x$, where $t$ is a positive real number depending only on $d,\epsilon$. We prove that Birkar's conjecture is equivalent to Shokurov's conjecture on boundedness of klt complements on Fano fibrations and we confirm Birkar's conjecture in dimension 2. As a corollary, we prove the boundedness of klt complements on Fano fibrations over surfaces.
Submission history
From: Bingyi Chen [view email][v1] Sat, 2 Mar 2024 09:47:01 GMT (833kb)
[v2] Tue, 9 Apr 2024 09:13:07 GMT (30kb)
[v3] Fri, 26 Apr 2024 14:51:08 GMT (30kb)
Link back to: arXiv, form interface, contact.