Boundedness of varieties of Fano type with alpha-invariants and volumes bounded below

Abstract

We show that fixed dimensional klt weak Fano pairs with alpha-invariants and volumes bounded away from $0$ and the coefficients of the boundaries belong to the set of hyperstandard multiplicities $\Phi (\mathcal{R})$ associated to a fixed finite set $\mathcal{R}$ form a bounded family. We also show $\alpha (X,B{)}^{d-1}\mathrm{vol}(-(K_X+B))$ are bounded from above for all klt weak Fano pairs $(X,B)$ of a fixed dimension $d$.

arXiv comment17 pages

References in corpus (1)

• Boundedness of $\mathbb{Q}$-Fano varieties with degrees and alpha-invariants bounded from below

Cited by in corpus (6)

• Optimal destabilization of K-unstable Fano varieties via stability thresholds
• Uniqueness of K-polystable degenerations of Fano varieties
• The existence of the Kähler-Ricci soliton degeneration
• On properness of K-moduli spaces and optimal degenerations of Fano varieties
• Equivariant K-stability under finite group action
• Boundedness results for singular Fano varieties and applications to Cremona groups