We show that for a K-unstable Fano variety, any divisorial valuation computing its stability threshold induces a nontrivial special test configuration preserving the stability threshold. When such a divisorial valuation exists, we show that the Fano variet ...
Let (X, Delta) be a projective log canonical Calabi-Yau pair and L an ample Q-line bundle on X, we show that there is a correspondence between lc places of (X, Delta) and weakly special test configurations of (X, Delta; L). ...
Let (X, A) be a strictly lc log Fano pair, we show that every lc place of complements of (X, A) is dreamy and there exists a correspondence between weakly special test configurations of (X, A; -KX - A) and lc places of complements of (X, A). ...
For a given K-polystable Fano variety X and a natural number l such that (X, 1/l B) is log canonical for some B ∈ | − lKX|, we show that there exists a rational number 0 < c1 < 1 depending only on X and l, such that D ∈ | − lKX| is GIT-(semi/poly)stable un ...
In this paper, we explore the wall crossing phenomenon for K-stability, and apply it to explain the wall crossing for K -moduli stacks and K-moduli spaces. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY li ...
In this note, we prove effective semi-ampleness conjecture due to Prokhorov and Shokurov for a special case, more concretely, for Q-Gorenstein klt-trivial fibrations over smooth projective curves whose fibers are all klt log Calabi-Yau pairs of Fano type. ...
We show that delta invariant of a log Fano pair can be approximated by lc places of plt complements if it is no greater than one. Under the assumption that delta invariant (no greater than one) of a log Fano pair can be approximated by lc places of bounded ...