Projective geometry - from foundations to applications

  title={Projective geometry - from foundations to applications},
  author={A. Beutelspacher and Ute Rosenbaum},
1. Synthetic geometry 2. Analytic geometry 3. The representation theorems 4. Quadratic sets 5. Applications of geometry to coding theory 6. Applications of geometry in cryptography. 
Finite Geometry and Combinatorial Applications
1. Fields 2. Vector spaces 3. Forms 4. Geometries 5. Combinatorial applications 6. The forbidden subgraph problem 7. MDS codes Appendix A. Solutions to the exercises Appendix B. Additional proofsExpand
Generalized Elliptic Cubic Curves, Part 1
We define the concept of Generalized Elliptic Cubic Curve (GECC) which is not necessarily embedded in a projective plane and which appears as an Incidence Geometry. We develop foundations and raiseExpand
Pappus' configuration in non commutative projective geometry with application to a theorem of A. Schleiermacher
An improvement of a theorem of Adolf Schleiermacher is given, using a particular projectivity that is a product of three perspectivities.
A common characterization of the projective spaces PG(4, n) and PG(5, n)
A common characterization of the projective spaces PG(4, n) and PG(5, n) in terms of finite irreducible planar spaces is given.
Hyperbolic geometry
This textbook is an introductory course on hyperbolic geometry, intended for students at the advanced undergraduate (Bachelor) or early graduate (Master) level.
Finite Projective Geometries and Linear Codes
In this paper, we study the connections between linear codes and projective geometries over finite fields. Often good codes come from interesting structures in projective geometries. For example, MDSExpand
Motivated by the fundamental results of the geometric algebra we study quadrila- teral lattices in projective spaces over division rings. After giving the noncommutative discrete Darboux equations weExpand
On the size of the automorphism group of a plane algebraic curve
Abstract Let K be an algebraically closed field of characteristic p > 0 , and let X be a curve over K of genus g ≥ 2 . Assume that p > 2 and that X admits a non-singular plane model. The followingExpand
The affine and projective groups are maximal
We show that the groups AGL_n(Q) and PGL_n(Q), seen as closed subgroups of S_{\infty}, are maximal-closed.
MUBs: From Finite Projective Geometry to Quantum Phase Enciphering
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space ofExpand


Geometry and Codes
1. Rational Codes.- 2. Decoding and Rational Approximations.- 3. Algebraic Curves.- 4. Generalized Jacobian Codes.- References.
Projective Geometries Over Finite Fields
1. Finite fields 2. Projective spaces and algebraic varieties 3. Subspaces 4. Partitions 5. Canonical forms for varieties and polarities 6. The line 7. First properties of the plane 8. Ovals 9.Expand
Applications of Finite Geometry to Cryptography
In this paper we survey several applications of classical geometric structures to cryptology. Particularly we shall deal with authentication schemes, threshold schemes, network problems andExpand
On the foundations of polar geometry
One of the two Buekenhout-Shult theorems for polar spaces required a finite rank assumption. Here we get rid of that restriction. Similarly, the polar spaces of possibly infinite rank having someExpand
A proof of the theorem of Pappus in finite Desarguesian affine planes
Without using the representation theorem and a theorem of J.H.M. WEDDERBURN we show that every finite Desarguesian affine plane is Pappian.
A defense of the honour of an unjustly neglected little geometry or a combinatorial approach to the projective plane of order five
In this paper, we consider the projective plane of order five from a combinatorial point of view. We shall see many of its properties (such as its uniqueness and existence, the order of the fullExpand
Finite projective spaces of three dimensions
This self-contained and highly detailed study considers projective spaces of three dimensions over a finite field. It is the second and core volume of a three-volume treatise on finite projectiveExpand
A First Course in Coding Theory
  • R. Hill
  • Mathematics, Computer Science
  • 1986
This book provides an elementary yet rigorous introduction to the theory of error-correcting codes, based on courses given by the author over several years to advanced undergraduates and first-year graduated students. Expand
Cryptography - theory and practice
  • D. Stinson
  • Computer Science
  • Discrete mathematics and its applications series
  • 1995
The object of the book is to produce a general, comprehensive textbook that treats all the essential core areas of cryptography. Expand
On the foundations of incidence geometry
The tremendous and sudden development of diagram geometries and related concepts such as chamber systems, combinatorial maps, incidence complexes (see for instance [2], [14], [15], [3]) and theirExpand