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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 476, Pages 92–110 (Mi znsl6726)  
Legendrian curves in $\mathbb C P^3$: cubics and curves on a quadric surface

N. Kalinin

National Research University Higher School of Economics, Soyuza Pechatnikov str. 16, St. Petersburg, Russia
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Abstract: We prove that the number of Legendrian rational cubics in ${\mathbb C P^3}$ through three generic points and a line is three. Also, we classify all Legendrian curves on a quadric surface. Additionally, several computations are verified using Macaulay2 computer algebra system.
Key words and phrases: complex contact structure, Legendrian curve.
Funding agency Grant number
HSE Basic Research Program
Support from the Basic Research Program of the National Research University Higher School of Economics is gratefully acknowledged. Supported in part by the Young Russian Mathematics award.
Received: 26.10.2018
Document Type: Article
UDC: 512.7
Language: English
Citation: N. Kalinin, “Legendrian curves in $\mathbb C P^3$: cubics and curves on a quadric surface”, Geometry and topology. Part 13, Zap. Nauchn. Sem. POMI, 476, POMI, St. Petersburg, 2018, 92–110
Citation in format AMSBIB
\Bibitem{Kal18}
\by N.~Kalinin
\paper Legendrian curves in $\mathbb C P^3$: cubics and curves on a quadric surface
\inbook Geometry and topology. Part~13
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 476
\pages 92--110
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6726}
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