An Introduction to Pure Projective Geometry.
Abstract
This work presents a synthetic account of an introductory course in projective geometry on the complex projective plane. It covers classical topics of projective correspondences in one-dimensional forms (linear and quadratic ranges of points and pencils of lines) and two-dimentional forms (homographies of the plane). The results have been drawn from various monographs, with some of them presented in the author's own treatment (for example, the topic of reciprocators -- conics with respect to which two given conics are polar conjugates). The new developments are presented in the concluding section on the geometric properties of plane homographies, where the concepts of a directing field and a transversal projecion of a homography are introdused.
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BibTeX
@misc{avksentyev2026introduction,
title = {{An Introduction to Pure Projective Geometry.}},
author = {Evgeny A. Avksentyev},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05804875v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Introduction to Pure Projective Geometry.
AU - Evgeny A. Avksentyev
PY - 2026
DA - 2026/10/18
PB - HAL
UR - https://hal.science/hal-05804875v1
AB - This work presents a synthetic account of an introductory course in projective geometry on the complex projective plane. It covers classical topics of projective correspondences in one-dimensional forms (linear and quadratic ranges of points and pencils of lines) and two-dimentional forms (homographies of the plane). The results have been drawn from various monographs, with some of them presented in the author's own treatment (for example, the topic of reciprocators -- conics with respect to which two given conics are polar conjugates). The new developments are presented in the concluding section on the geometric properties of plane homographies, where the concepts of a directing field and a transversal projecion of a homography are introdused.
ER -