Log Canonical Thresholds of Complete Intersection Log Del Pezzo Surfaces

2015 ◽  
Vol 58 (2) ◽  
pp. 445-483 ◽  
Author(s):  
In-Kyun Kim ◽  
Jihun Park
Keyword(s):  
Complete Intersection ◽  
Einstein Metrics ◽  
Projective Spaces ◽  
Del Pezzo Surfaces ◽  
Log Canonical ◽  
Del Pezzo ◽  
Kähler Einstein Metrics ◽  
Log Del Pezzo Surfaces

AbstractWe compute the global log canonical thresholds of quasi-smooth well-formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As a corollary we show the existence of orbifold Kähler—Einstein metrics on many of them.

Weakly exceptional singularities of log del Pezzo surfaces

2019 ◽  
Vol 30 (01) ◽  
pp. 1950010
Author(s):  
In-Kyun Kim ◽  
Joonyeong Won
Keyword(s):  
Complete Intersection ◽  
Projective Spaces ◽  
Pezzo Surface ◽  
Del Pezzo Surfaces ◽  
Del Pezzo Surface ◽  
Log Canonical ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

We complete the computation of global log canonical thresholds, or equivalently alpha invariants, of quasi-smooth well-formed complete intersection log del Pezzo surfaces of amplitude 1 in weighted projective spaces. As an application, we prove that they are weakly exceptional. And we investigate the super-rigid affine Fano 3-folds containing a log del Pezzo surface as boundary.

scholarly journals Toric log del Pezzo surfaces with one singularity

2020 ◽  
Vol 20 (1) ◽  
pp. 121-138
Author(s):  
Dimitrios I. Dais
Keyword(s):  
Projective Spaces ◽  
Del Pezzo Surfaces ◽  
Del Pezzo ◽  
Log Del Pezzo Surfaces

AbstractThis paper focuses on the classification (up to isomorphism) of all toric log Del Pezzo surfaces with exactly one singularity, and on the description of how they are embedded as intersections of finitely many quadrics into suitable projective spaces.

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