TY - GEN

T1 - Algebraic Surfaces and Their Geometric Bases

AU - Manevich, Michael

AU - Itskovich, Elizabeth

N1 - 20th International Conference on Geometry and Graphics (ICGG), ELECTR NETWORK, AUG 15-19, 2022

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Projective correspondences

KW - Projective rows of points

KW - Double points

KW - Extensive equations

UR - http://www.scopus.com/inward/record.url?scp=85136305844&partnerID=8YFLogxK

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SN - 978-3-031-13588-0; 978-3-031-13587-3

VL - 146

T3 - Lecture Notes on Data Engineering and Communications Technologies

SP - 228

EP - 237

BT - ICGG 2022 - PROCEEDINGS OF THE 20TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS

A2 - Cheng, LY

PB - Springer International Publishing AG

CY - GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND

ER -