Exceptional del Pezzo hypersurfaces
Ivan Cheltsov, Jihun Park, Constantin Shramov

TL;DR
This paper calculates the global log canonical thresholds for a broad class of quasismooth del Pezzo hypersurfaces in weighted projective spaces, leading to new existence results for orbifold Kähler--Einstein metrics and classifications of exceptional cases.
Contribution
It provides explicit computations of thresholds, establishes existence of Kähler--Einstein metrics, and classifies exceptional hypersurfaces in weighted projective spaces.
Findings
Computed thresholds for many hypersurfaces
Established existence of orbifold Kähler--Einstein metrics
Classified exceptional and weakly exceptional hypersurfaces
Abstract
We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in . As a corollary we obtain the existence of orbifold K\"ahler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-formed del Pezzo weighted hypersurfaces in .
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory
