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Log Canonical Thresholds of Complete Intersection Log Del Pezzo Surfaces

Part of: Complex manifolds Surfaces and higher-dimensional varieties Computational aspects in algebraic geometry Special varieties

Published online by Cambridge University Press:  20 February 2015

In-Kyun Kim  and
Jihun Park
In-Kyun Kim
Affiliation:
Center for Geometry and Physics, Institute for Basic Science, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 790-784, Republic of Korea Department of Mathematics, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 790-784, Republic of Korea, (wlog@postech.ac.kr; soulcraw@gmail.com)
Jihun Park
Affiliation:
Center for Geometry and Physics, Institute for Basic Science, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 790-784, Republic of Korea Department of Mathematics, Pohang University of Science and Technology, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk 790-784, Republic of Korea, (wlog@postech.ac.kr; soulcraw@gmail.com)
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Abstract

We 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.

Keywords

global log canonical thresholdweighted complete intersectionα-invariantKähler—Einstein metricexceptional Fano varietyweakly exceptional Fano variety

MSC classification

Primary: 14M10: Complete intersections 14J45: Fano varieties 14J17: Singularities
Secondary: 14Q10: Surfaces, hypersurfaces 32Q20: Kähler-Einstein manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 2 , June 2015 , pp. 445 - 483
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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