Duality of planar and spacial curves: new insight

Viktor S. Kulikov*, Eugenii Shustin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the geometry of equiclassical strata of the discriminant in the space of plane curves of a given degree, which are families of curves of given degree, genus and class (degree of the dual curve). Our main observation is that the use of duality transformation leads to a series of new sufficient conditions for a regular behavior of the equiclassical stratification. We also discuss duality of curves in higher-dimensional projective spaces and in Grassmannians with focus on similar questions of the regularity of equiclassical families of spacial curves.

Original languageEnglish
Pages (from-to)462-482
Number of pages21
JournalEuropean Journal of Mathematics
Issue number3
StatePublished - 1 Sep 2015


  • Duality of curves
  • Equiclassical stratification
  • Planar curves
  • Spacial curves


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