Displaying similar documents to “Existence problem of the osculating planes of a curve in R n

Structure of the McMullen domain in the parameter planes for rational maps

Robert L. Devaney (2005)

Fundamenta Mathematicae

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We show that, for the family of functions F λ ( z ) = z + λ / z where n ≥ 3 and λ ∈ ℂ, there is a unique McMullen domain in parameter space. A McMullen domain is a region where the Julia set of F λ is homeomorphic to a Cantor set of circles. We also prove that this McMullen domain is a simply connected region in the plane that is bounded by a simple closed curve.

On ramified covers of the projective plane II: Generalizing Segre’s theory

Michael Friedman, Rebecca Lehman, Maxim Leyenson, Mina Teicher (2012)

Journal of the European Mathematical Society

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The classical Segre theory gives a necessary and sufficient condition for a plane curve to be a branch curve of a (generic) projection of a smooth surface in 3 . We generalize this result for smooth surfaces in a projective space of any dimension in the following way: given two plane curves, B and E , we give a necessary and sufficient condition for B to be the branch curve of a surface X in N and E to be the image of the double curve of a 3 -model of X . In the classical Segre theory, a...

Finite projective planes, Fermat curves, and Gaussian periods

Koen Thas, Don Zagier (2008)

Journal of the European Mathematical Society

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One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences...

Recovering an algebraic curve using its projections from different points. Applications to static and dynamic computational vision

Jeremy Yirmeyahu Kaminski, Michael Fryers, Mina Teicher (2005)

Journal of the European Mathematical Society

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We study some geometric configurations related to projections of an irreducible algebraic curve embedded in 3 onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve X embedded in 3 , of degree d and genus g , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining...

A curve of genus q with a Half-Canonical embedding in 𝐏 3

Sevin Recillas (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si costruiscono curve di genere g = 4 n 3 , n 3 che hanno 2 n - 3 ( 2 n - 2 - 1 ) fasci semicanonici L tali che h 0 ( L ) = 4 . Per n + 3 si dimostra che gli L sono molto ampi.

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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Polyhedral Realization of a Thurston Compactification

Matthieu Gendulphe, Yohei Komori (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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Let Σ 3 - be the connected sum of three real projective planes. We realize the Thurston compactification of the Teichmüller space Teich ( Σ 3 - ) as a simplex in P ( 4 ) .