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European Journal of Mathematics

, Volume 5, Issue 3, pp 622–639 | Cite as

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

  • Valery AlexeevEmail author
  • Wenfei Liu
Research Article
  • 5 Downloads

Abstract

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.

Keywords

Log canonical surfaces Volume Four-line configuration 

Mathematics Subject Classification

14J29 14J26 14R05 

Notes

References

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    Alexeev, V.A., Liu, W.: On accumulation points of volumes of log surfaces. Izv Math. 83 (2019).  https://doi.org/10.1070/IM8842
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    Alexeev, V., Mori, S.: Bounding singular surfaces of general type. In: Christensen, C., et al. (eds.) Algebra, Arithmetic and Geometry with Applications, pp. 143–174. Springer, Berlin (2004)CrossRefGoogle Scholar
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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China

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