Abstract
This article introduces the concept of a geometric basis for algebraic surfaces of the second and third orders, which allows to write their extensive Grassman equations. Points of the surface of third degree are double points of projective correspondences, which are established on the rays of the bundle of lines with the center at one of the points of the geometric basis. Coordinates of these double points are calculated using programs developed by the authors. Some questions related to the common elements of an algebraic surface and their geometric basis are considered. This work is a continuation of the article [8] presented at the conference in Milan in 2018.
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Acknowledgment
The authors would like to thank the referees for the valuable remarks and suggestions which helped to improve the paper.
Dedicated to dear brother Vladimir Manevich.
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Manevich, M., Itskovich, E. (2023). Algebraic Surfaces and Their Geometric Bases. In: Cheng, LY. (eds) ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. ICGG 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-031-13588-0_20
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DOI: https://doi.org/10.1007/978-3-031-13588-0_20
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