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Annals of Global Analysis and Geometry

, Volume 55, Issue 3, pp 555–573 | Cite as

Twistor lines on algebraic surfaces

  • A. AltavillaEmail author
  • E. Ballico
Article

Abstract

We give quantitative and qualitative results on the family of surfaces in \(\mathbb {CP}^3\) containing finitely many twistor lines. We start by analyzing the ideal sheaf of a finite set of disjoint lines E. We prove that its general element is a smooth surface containing E and no other line. Afterward we prove that twistor lines are Zariski dense in the Grassmannian Gr(2, 4). Then, for any degree \(d\ge 4\), we give lower bounds on the maximum number of twistor lines contained in a degree d surface. The smooth and singular cases are studied as well as the j-invariant one.

Keywords

Twistor fibration Lines on surfaces Plücker quadric 

Mathematics Subject Classification

Primary 14D21 53C28 Secondary 32L25 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Dipartimento Di MatematicaUniversità di Roma “Tor Vergata”RomeItaly
  2. 2.Dipartimento Di MatematicaUniversità di TrentoPovo, TrentoItaly

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