Minimal degree equations for curves and surfaces (variations on a theme of Halphen)

  • Edoardo Ballico
  • Emanuele VenturaEmail author
Original Paper


Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such collections of varieties: their minimal degree and their maximal number of linearly independent smallest degree hypersurfaces passing through them. We show results for curves and surfaces, and pose several questions.


Minimal degree equations Linear systems 

Mathematics Subject Classification

Primary 14N05 Secondary 14H50 14J25 



The first author was partially supported by MIUR and GNSAGA of INdAM (Italy). The second author would like to thank the Department of Mathematics of Università di Trento, where part of this project was conducted, for the warm hospitality. We are grateful to an anonymous referee for pointing out a mistake in an earlier version and providing useful comments.


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Copyright information

© The Managing Editors 2019

Authors and Affiliations

  1. 1.Università di TrentoPovoItaly
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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