Quadratic differentials of real algebraic curves

Alexander Solynin, Andrey Solynin

Research output: Contribution to journalArticlepeer-review


It was shown by J. C. Langer and D. A. Singer in their influential 2007 paper [5] that real algebraic curves can be interpreted as trajectories of meromorphic quadratic differentials defined on appropriate Riemann surfaces. The goal of this note is to suggest a more elementary approach to this problem that is based on the classical complex analysis. To demonstrate how our approach works, we apply it to the simplest non-trivial case of real algebraic curves; i.e. to conics.

Original languageEnglish
Article number125760
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Mar 1 2022


  • Conic
  • Ellipse
  • Hyperbola
  • Parabola
  • Quadratic differential
  • Real algebraic curve


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