Theoretical analysis establishes lower bounds for delta invariants in index-1 quasismooth Fano threefolds, demonstrating their complete K-stability.
We settle the problem of K-stability of quasismooth Fano 3-fold hypersurfaces with Fano index 1 by providing lower bounds for their delta invariants. We use the method introduced by Abban and Zhuang for computing lower bounds of delta invariants on flags of hypersurfaces in the Fano 3-fold.
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Campo et al. (2026) studied this question.
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