Algebraic Surfaces and Their Geometric Bases

Michael Manevich; Elizabeth Itskovich

Algebraic Surfaces and Their Geometric Bases

Michael Manevich, Elizabeth Itskovich

Department of Industrial Engineering and Management

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	ICGG 2022 - PROCEEDINGS OF THE 20TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS
Editors	LY Cheng
Place of Publication	GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND
Publisher	Springer International Publishing AG
Pages	228-237
Number of pages	10
Volume	146
ISBN (Print)	978-3-031-13588-0; 978-3-031-13587-3
State	Published - 2023

Publication series

Name	Lecture Notes on Data Engineering and Communications Technologies
Publisher	SPRINGER INTERNATIONAL PUBLISHING AG

Keywords

Projective correspondences
Projective rows of points
Double points
Extensive equations

Access to Document

https://link.springer.com/chapter/10.1007/978-3-031-13588-0_20

Cite this

Manevich, M., & Itskovich, E. (2023). Algebraic Surfaces and Their Geometric Bases. In LY. Cheng (Ed.), ICGG 2022 - PROCEEDINGS OF THE 20TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS (Vol. 146, pp. 228-237). (Lecture Notes on Data Engineering and Communications Technologies). Springer International Publishing AG. https://link.springer.com/chapter/10.1007/978-3-031-13588-0_20

Manevich, Michael ; Itskovich, Elizabeth. / Algebraic Surfaces and Their Geometric Bases. ICGG 2022 - PROCEEDINGS OF THE 20TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS. editor / LY Cheng. Vol. 146 GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND : Springer International Publishing AG, 2023. pp. 228-237 (Lecture Notes on Data Engineering and Communications Technologies).

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Manevich, M & Itskovich, E 2023, Algebraic Surfaces and Their Geometric Bases. in LY Cheng (ed.), ICGG 2022 - PROCEEDINGS OF THE 20TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS. vol. 146, Lecture Notes on Data Engineering and Communications Technologies, Springer International Publishing AG, GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND, pp. 228-237. <https://link.springer.com/chapter/10.1007/978-3-031-13588-0_20>

Algebraic Surfaces and Their Geometric Bases. / Manevich, Michael; Itskovich, Elizabeth.
ICGG 2022 - PROCEEDINGS OF THE 20TH INTERNATIONAL CONFERENCE ON GEOMETRY AND GRAPHICS. ed. / LY Cheng. Vol. 146 GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND: Springer International Publishing AG, 2023. p. 228-237 (Lecture Notes on Data Engineering and Communications Technologies).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Algebraic Surfaces and Their Geometric Bases

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