Volumes of integral divisors on epsilon-lc Calabi-Yau pairs lie in a fixed discrete set, settling Birkar's boundedness conjecture for polarized log Calabi-Yau pairs.
On connectedness of non-klt loci of singularities of pairs
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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 $Z$, the non-klt locus of $(X,B)$ has at most two connected components near each fibre of $X\to Z$. This was conjectured by Hacon and Han. In a different direction we answer a question of Mark Gross on connectedness of the non-klt loci of certain pairs. This is motivated by constructions in Mirror Symmetry.
fields
math.AG 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Discreteness of volumes of divisors on Calabi-Yau type varieties
Volumes of integral divisors on epsilon-lc Calabi-Yau pairs lie in a fixed discrete set, settling Birkar's boundedness conjecture for polarized log Calabi-Yau pairs.