Naslov
Circular Quartics in the Isotropic Plane Generated by Projectively Linked Pencils of Conics

Autori
Jurkin, Ema

Izvornik
Acta mathematica Hungarica (0236-5294) 130 (2011), 1-2; 35-49

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
isotropic plane; circular quartic; projectivity; pencils of conics

Sažetak
A curve in the isotropic plane is circular if it passes through the absolute point F. Its degree of circularity is defined as the number of its intersection points with the absolute line f falling into the absolute point F. A curve of order four can be obtained as a locus of the intersections of corresponding conics of projectively linked pencils of conics. In this paper the conditions that the pencils and the projectivity have to fulfill in order to obtain a circular quartic of a certain degree of circularity have been determined analytically. The quartics of all degrees of circularity and all types (depending on their position with respect to the absolute figure) can be constructed using these results. The results have first been stated for any projective plane and then their isotropic interpretation has been given.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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