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, 2020, Volume 56, Issue 3, Pages 539–559
(Mi prims1)
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This article is cited in 4 scientific papers (total in 4 papers)
Boundedness of weak Fano pairs with alpha-invariants and volumes bounded below
W. Chen University of Tokyo, Japan
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 belonging to the set of hyperstandard multiplicities $\Phi(\mathscr R)$ associated to a fixed finite set $\mathscr R$ 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 $d$.
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