4 papers · 1 filter
Open problems in K-stability of Fano varieties
Chenyang Xu, Ziquan Zhuang
In this note, we discuss a number of open problems in K-stability theory.
Relative stability theory and properness of K-moduli spaces
Harold Blum, Yuchen Liu, Chenyang Xu +1
We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-…
Irreducible symplectic varieties with a large second Betti number
Yuchen Liu, Zhiyu Liu, Chenyang Xu
We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian f…
Boundedness of log Fano cone singularities and discreteness of local volumes
Chenyang Xu, Ziquan Zhuang
We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence,…