K-stablity of Fano threefold hypersurfaces of index 1
Livia Campo, Takuzo Okada
TL;DR
This paper establishes the K-stability of certain Fano threefold hypersurfaces with index 1 by deriving lower bounds for their delta invariants using a specialized computational method.
Contribution
It provides the first comprehensive proof of K-stability for these Fano 3-fold hypersurfaces through explicit delta invariant bounds.
Findings
Confirmed K-stability for all quasi-smooth Fano 3-fold hypersurfaces of index 1
Developed a method to compute delta invariants on hypersurface flags
Established lower bounds for delta invariants that imply stability
Abstract
We settle the problem of K-stability of quasi-smooth 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric and Algebraic Topology