Unstable singular del Pezzo hypersurfaces with lower index
In-kyun Kim, Joonyeong Won
TL;DR
This paper presents examples of singular del Pezzo surfaces with index 2 that are K-unstable and are realized as weighted hypersurfaces, contributing to the understanding of stability in algebraic geometry.
Contribution
It provides explicit examples of K-unstable singular del Pezzo hypersurfaces with lower index, expanding the known classifications.
Findings
Identified K-unstable singular del Pezzo hypersurfaces with index 2
Constructed explicit weighted hypersurface examples
Enhanced understanding of stability conditions for del Pezzo surfaces
Abstract
We give examples of K-unstable singular del Pezzo surfaces which are weighted hypersurfaces with index 2.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Holomorphic and Operator Theory