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A weak Fano threefold arising as a blowup of a curve of genus 5 and degree 8 on \({\mathbb {P}}^3\)

  • Joseph W. CutroneEmail author
  • Michael A. Limarzi
  • Nicholas A. Marshburn
Research Article
  • 3 Downloads

Abstract

This article constructs a smooth weak Fano threefold of Picard number two with small anticanonical morphism that arises as a blowup of a smooth curve of genus 5 and degree 8 in \({\mathbb {P}}^3\). While the existence of this weak Fano was known as a numerical possibility in Cutrone and Marshburn (Cent Eur J Math 11(9):1552–1576, 2013) and constructed in Blanc and Lamy (Proc Lond Math Soc 105(5):1047–1075, 2012), this paper removes the dependencies on the results in Jahnke et al. (Cent Eur J Math 9(3):449–488, 2011) needed in the construction of Blanc and Lamy (Proc Lond Math Soc 105(5):1047–1075, 2012) and constructs the link in the style of Arap et al. (Math Scand 120(1):68–86, 2017).

Keywords

Weak Fano threefold Sarkisov link Type E1–E1 

Mathematics Subject Classification

14E05 14E08 14E30 

Notes

Acknowledgements

The authors express their gratitude to Iran Cheltsov for both posing the problem and subsequent discussions that followed. In addition, we would like to thank all the organizers of the Workshop in Algebraic Geometry held on December 18–22, 2016, in Hanga Roa, Chile.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Joseph W. Cutrone
    • 1
    Email author
  • Michael A. Limarzi
    • 2
  • Nicholas A. Marshburn
    • 3
  1. 1.Center for Data, Mathematical, and Computational SciencesGoucher CollegeBaltimoreUSA
  2. 2.Department of Mathematics and StatisticsAmerican UniversityWashingtonUSA
  3. 3.Center for Talented YouthJohns Hopkins UniversityBaltimoreUSA

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