TY - JOUR

T1 - Quadratic differentials of real algebraic curves

AU - Solynin, Alexander

AU - Solynin, Andrey

PY - 2022/3/1

Y1 - 2022/3/1

N2 - 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.

AB - 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.

KW - Real algebraic curve

KW - Quadratic differential

KW - Conic

KW - Ellipse

KW - Hyperbola

KW - Parabola

KW - CLASSIFICATION

UR - http://www.scopus.com/inward/record.url?scp=85117127688&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/95114f25-fbc8-34f6-959d-03603b95cbcc/

U2 - 10.1016/j.jmaa.2021.125760

DO - 10.1016/j.jmaa.2021.125760

M3 - Article

VL - 507

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

M1 - 125760

ER -