Let be a pair, and let be a contraction with nef over S. A conjecture, known as the Shokurov–
Kollár connectedness principle, predicts that has at most two connected components, where …

We prove the existence of flips for $\mathbb Q $-factorial NQC generalized lc pairs, and the
cone and contraction theorems for NQC generalized lc pairs. This answers a question of C …

We study the behavior of generalized lc pairs with b-log abundant nef part, a meticulously
designed structure on algebraic varieties. We show that this structure is preserved under the …

We study the non-klt locus of singularities of pairs. We show that given a pair $(X, B) $ and a
projective morphism $ X\to Z $ with connected fibres such that $-(K_X+ B) $ is nef over $ Z …

We develop a framework that allows one to describe the birational geometry of Calabi-Yau
pairs $(X, D) $. After establishing some general results for Calabi-Yau pairs $(X, D) $ with …

In this paper, we study the theory of complements, introduced by Shokurov, for Calabi–Yau
type varieties with the coefficient set [0, 1]. We show that there exists a finite set of positive …

We expand the theory of log canonical $3 $-fold complements. We prove that if $
X\rightarrow T $ is a $3 $-dimensional contraction of log Calabi-Yau type, then we can find …

We study the non‑klt locus of singularities of pairs. We show that given a pair $(X, B) $ and a
projective morphism $ X\to Z $ with connected fibres such that $-(K_X+ B) $ is nef over $ Z …

We prove the termination of flips for pseudo-effective NQC log canonical generalized pairs
of dimension 4. As main ingredients, we verify the termination of flips for 3-dimensional NQC …

Fano-type surfaces with large cyclic automorphisms Page 1 Forum of Mathematics, Sigma (2021),
Vol. 9:e54 1–27 doi:10.1017/fms.2021.44 RESEARCH ARTICLE Fano-type surfaces with …