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Arnold Mathematical Journal

, Volume 4, Issue 3–4, pp 345–414 | Cite as

Deformation Classification of Real Non-singular Cubic Threefolds with a Marked Line

  • S. Finashin
  • V. KharlamovEmail author
Research Contribution
  • 13 Downloads

Abstract

We prove that the space of pairs (Xl) formed by a real non-singular cubic hypersurface \(X\subset P^4\) with a real line \(l\subset X\) has 18 connected components and give for them several quite explicit interpretations. The first one relates these components to the orbits of the monodromy action on the set of connected components of the Fano surface \(F_{\mathbb R}(X)\) formed by real lines on X. For another interpretation we associate with each of the 18 components a well defined real deformation class of real non-singular plane quintic curves and show that this deformation class together with the real deformation class of X characterizes completely the component.

Keywords

Real cubic threefolds Fano surfaces of real lines Real plane quintics Real theta-characteristics Real deformation classification Monodromy 

Mathematics Subject Classification

Primary 14P25 14J10 14N25 14J30 14J70 

Notes

Acknowledgements

This work was done during visits of the first author to the University of Strasbourg and joint visits to the Max Planck Institute in Bonn and the Mathematisches Forschungsinstitut Oberwolfach. We thank all these institutions for providing excellent working conditions.

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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Université de Strasbourg et IRMA (CNRS)Strasbourg CedexFrance

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