The point and line space of a compact projective plane are homeomorphic

2000 ◽  
Vol 234 (1) ◽  
pp. 83-102
Author(s):  
Linus Kramer
Keyword(s):  
Projective Plane ◽  
Compact Projective Plane ◽  
Line Space

Compactness in Topological Hjelmslev Planes

1984 ◽  
Vol 27 (4) ◽  
pp. 423-429 ◽  
Author(s):  
J. W. Lorimer
Keyword(s):  
Projective Plane ◽  
Affine Plane ◽  
Projective Planes ◽  
Coordinate Ring ◽  
Locally Compact ◽  
Compact Projective Plane ◽  
Negative Results ◽  
Connected Projective Plane ◽  
Topological Affine

AbstractIn the theory of ordinary topological affine and projective planes it is known that (1) An affine plane is never compact (2) a locally compact ordered projective plane is compact and archimedean (3) a locally compact connected projective plane is compact and (4) a locally compact projective plane over a coordinate ring with bi-associative multiplication is compact. In this paper we re-examine these results within the theory of topological Hjelmslev Planes and observe that while (1) remains valid (2), (3) and (4) are false. At first glance these negative results seem to suggest we are working in too general a setting. However a closer examination reveals that the absence of compactness in our setting is a natural and expected feature which in no way precludes the possibility of obtaining significant results.

Gilles Deleuze's Luminous Philosophy

2020 ◽  
Author(s):  
Hanjo Berressem
Keyword(s):  
Projective Plane ◽  
Visual Arts ◽  
Whole Body ◽  
Literary Studies ◽  
Chronological Order ◽  
Real Projective Plane ◽  
Cinema Studies ◽  
The Real

Providing a comprehensive reading of Deleuzian philosophy, Gilles Deleuze’s Luminous Philosophy argues that this philosophy’s most consistent conceptual spine and figure of thought is its inherent luminism. When Deleuze notes in Cinema 1 that ‘the plane of immanence is entirely made up of light’, he ties this philosophical luminism directly to the notion of the complementarity of the photon in its aspects of both particle and wave. Engaging, in chronological order, the whole body and range of Deleuze’s and Deleuze and Guattari’s writing, the book traces the ‘line of light’ that runs through Deleuze’s work, and it considers the implications of Deleuze’s luminism for the fields of literary studies, historical studies, the visual arts and cinema studies. It contours Deleuze’s luminism both against recent studies that promote a ‘dark Deleuze’ and against the prevalent view that Deleuzian philosophy is a philosophy of difference. Instead, it argues, it is a philosophy of the complementarity of difference and diversity, considered as two reciprocally determining fields that are, in Deleuze’s view, formally distinct but ontologically one. The book, which is the companion volume toFélix Guattari’s Schizoanalytic Ecology, argues that the ‘real projective plane’ is the ‘surface of thought’ of Deleuze’s philosophical luminism.

Anastigmatic design of imaging spectrometer with varied line-space convex grating

2020 ◽  
Vol 28 (10) ◽  
pp. 2103-2111
Author(s):  
Mei-hong ZHAO ◽  
◽  
Xin-yu WANG ◽  
Yan-xiu JIANG ◽  
Shuo YANG ◽  
...  
Keyword(s):  
Imaging Spectrometer ◽  
Line Space

scholarly journals Group-labeled light dual multinets in the projective plane

2018 ◽  
Vol 341 (8) ◽  
pp. 2121-2130 ◽  
Author(s):  
Gábor Korchmáros ◽  
Gábor P. Nagy
Keyword(s):  
Projective Plane

scholarly journals Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane

2021 ◽  
pp. 104255
Author(s):  
Rodrigo A. von Flach ◽  
Marcos Jardim ◽  
Valeriano Lanza
Keyword(s):  
Projective Plane ◽  
Moduli Spaces ◽  
Obstruction Theory

AN INTERPRETATION OF LINE GEOMETRY ON PROJECTIVE PLANE

1994 ◽  
Vol 27 (1) ◽  
Author(s):  
Edwin Kozniewski
Keyword(s):  
Projective Plane ◽  
Line Geometry

scholarly journals On 3-syzygy and unexpected plane curves

2021 ◽  
Author(s):  
Grzegorz Malara ◽  
Piotr Pokora ◽  
Halszka Tutaj-Gasińska
Keyword(s):  
Projective Plane ◽  
Plane Curves ◽  
Complex Projective Plane ◽  
Geometric Properties ◽  
Complex Projective

AbstractIn this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties. More generally, we study 3-syzygy curve arrangements and we present examples that admit unexpected curves.

Divisible Semiplanes, Arcs, and Relative Difference Sets

1987 ◽  
Vol 39 (4) ◽  
pp. 1001-1024 ◽  
Author(s):  
Dieter Jungnickel
Keyword(s):  
Projective Plane ◽  
Difference Sets ◽  
Difference Set ◽  
Relative Difference ◽  
List Type ◽  
Relative Difference Set ◽  
Large Collection ◽  
Baer Subplane ◽  
Relative Difference Sets ◽  
Definition Of

In this paper we shall be concerned with arcs of divisible semiplanes. With one exception, all known divisible semiplanes D (also called “elliptic” semiplanes) arise by omitting the empty set or a Baer subset from a projective plane Π, i.e., D = Π\S, where S is one of the following:(i) S is the empty set.(ii) S consists of a line L with all its points and a point p with all the lines through it.(iii) S is a Baer subplane of Π.We will introduce a definition of “arc” in divisible semiplanes; in the examples just mentioned, arcs of D will be arcs of Π that interact in a prescribed manner with the Baer subset S omitted. The precise definition (to be given in Section 2) is chosen in such a way that divisible semiplanes admitting an abelian Singer group (i.e., a group acting regularly on both points and lines) and then a relative difference set D will always contain a large collection of arcs related to D (to be precise, —D and all its translates will be arcs).

scholarly journals Maximal arcs in projective planes of order 16 and related designs

2019 ◽  
Vol 19 (3) ◽  
pp. 345-351 ◽  
Author(s):  
Mustafa Gezek ◽  
Vladimir D. Tonchev ◽  
Tim Wagner
Keyword(s):  
Projective Plane ◽  
Projective Planes ◽  
Maximal Arcs ◽  
Even Order

Abstract The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising from maximal (120,8)-arcs, and the 2-(52,4,1) designs arising from previously known maximal (52,4)-arcs, as well as some newly discovered maximal (52,4)-arcs in the known projective planes of order 16, are computed. It is shown that each 2-(120,8,1) design associated with a maximal (120,8)-arc is embeddable in a unique way in a projective plane of order 16. This result suggests a possible strengthening of the Bose–Shrikhande theorem about the embeddability of the complement of a hyperoval in a projective plane of even order. The computations of the maximal sets of compatible resolutions of the 2-(52,4,1) designs associated with maximal (52,4)-arcs show that five of the known projective planes of order 16 contain maximal arcs whose associated designs are embeddable in two nonisomorphic planes of order 16.

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