Abstract
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 language | English |
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Article number | 125760 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 507 |
Issue number | 1 |
DOIs | |
State | Published - Mar 1 2022 |
Keywords
- Conic
- Ellipse
- Hyperbola
- Parabola
- Quadratic differential
- Real algebraic curve