Log surfaces of Picard rank one from four lines in the plane

We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blow-ups and contractions of the four-line configuration in the plane. As an application, we establish the smallest positive volume and the smallest accumulation point of volumes of...

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Bibliographic Details
Published in:European journal of mathematics 2019-09, Vol.5 (3), p.622-639
Main Authors: Alexeev, Valery, Liu, Wenfei
Format: Article
Language:English
Subjects:
Algebraic Geometry
Mathematics
Mathematics and Statistics
Research Article
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Summary:We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blow-ups and contractions of the four-line configuration in the plane. As an application, we establish the smallest positive volume and the smallest accumulation point of volumes of log canonical surfaces obtained in this way.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-019-00347-2