THE ANALYSIS OF IMAGES IN N-POINT GRAVITATIONAL LENS BY METHODS OF ALGEBRAIC GEOMETRY

Authors

  • Albert Kotvytskiy V. N. Karazin Kharkiv National University
  • Semen Bronza
  • Vladimir Shablenko V. N. Karazin Kharkiv National University

DOI:

https://doi.org/10.14311/AP.2017.57.0404

Keywords:

gravitational lenses, images, algebaric geometry, resultant

Abstract

This paper is devoted to the study of images in N-point gravitational lenses by methods of algebraic geometry. In the beginning, we carefully define images in algebraic terms. Based on the definition, we show that in this model of gravitational lenses (for a point source), the dimensions of the images can be only 0 and 1. We reduce it to the fundamental problem of classical algebraic geometry - the study of solutions of a polynomial system of equations. Further, we use well-known concepts and theorems. We adapt known or prove new assertions. Sometimes, these statements have a fairly general form and can be applied to other problems of algebraic geometry. In this paper: the criterion for irreducibility of polynomials in several variables over the field of complex numbers is effectively used. In this paper, an algebraic version of the Bezout theorem and some other statements are formulated and proved. We have applied the theorems proved by us to study the imaging of dimensions 1 and 0.

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Author Biographies

Albert Kotvytskiy, V. N. Karazin Kharkiv National University

Academician I.M.Lifshits Department of Theoretical Physics, Associate Professor

Semen Bronza

Ukrainian State University of Railway Transport

Department of Higher Mathematics

Associate Professor

Vladimir Shablenko, V. N. Karazin Kharkiv National University

Academician I.M.Lifshits Department of Theoretical Physics,student

 

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Published

2017-12-30

How to Cite

Kotvytskiy, A., Bronza, S., & Shablenko, V. (2017). THE ANALYSIS OF IMAGES IN N-POINT GRAVITATIONAL LENS BY METHODS OF ALGEBRAIC GEOMETRY. Acta Polytechnica, 57(6), 404–411. https://doi.org/10.14311/AP.2017.57.0404

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Articles