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

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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.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Georgia, Athens, GA, 30605, USA

    Valery Alexeev

  2. School of Mathematical Sciences, Xiamen University, Siming South Road 422, Xiamen, 361005, Fujian, People’s Republic of China

    Wenfei Liu

Authors
  1. Valery Alexeev
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  2. Wenfei Liu
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Correspondence to Valery Alexeev.

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The first author was supported by NSF Grant DMS-1603604. The second author was partially supported by the NSFC (Nos. 11501012 and 11771294).

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Alexeev, V., Liu, W. Log surfaces of Picard rank one from four lines in the plane. European Journal of Mathematics 5, 622–639 (2019). https://doi.org/10.1007/s40879-019-00347-2

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  • DOI: https://doi.org/10.1007/s40879-019-00347-2

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