The absolute regularity of a Fano variety, denoted by reg^(X), is the largest dimension of the
dual complex of a log Calabi–Yau structure on X. The absolute coregularity is defined to be …

The ACC conjecture for local volumes predicts that the set of local volumes of klt
singularities $ x\in (X,\Delta) $ satisfies the ACC if the coefficients of $\Delta $ belong to a …

In this article, we prove a toroidalization principle for finite actions on klt singularities. As an
application, we prove that the Jordan property for the regional fundamental group of klt …

Recent study in K-stability suggests that klt singularities whose local volumes are bounded
away from zero should be bounded up to special degeneration. We show that this is true in …

The main approach to study algebraic singularities is to introduce invariants that allow us to
measure how singular a point in an algebraic variety is. Once the invariant is introduced, the …

In this article, we use the cone of nef curves to study minimal log discrepancies. The first
result is an improvement of the nef cone theorem in the case of log Calabi–Yau dlt pairs …

Prokhorov and Shramov proved that the BAB conjecture, which Birkar later proved, implies
the uniform Jordan property for automorphism groups of complex Fano varieties of fixed …

We study the normalized volume of toric singularities. As it turns out, there is a close relation
to the notion of (nonsymmetric) Mahler volume from convex geometry. This observation …

We study Kawamata log terminal singularities of full rank, ie, $ n $-dimensional klt
singularities containing a large finite abelian group of rank $ n $ in its regional fundamental …

In this article we study conjectures regarding normalized volume and boundedness of
singularities. We focus on singularities with a torus action of complexity 1, threefold …