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- Title
Circular quartics in the isotropic plane generated by projectively linked pencils of conics.
- Authors
Jurkin, E.
- Abstract
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.
- Subjects
PROJECTIVE planes; QUARTIC fields; MATRIX pencils; CONIC sections; NUMBER theory; MATHEMATICAL analysis
- Publication
Acta Mathematica Hungarica, 2011, Vol 130, Issue 1/2, p35
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-010-0038-2