Geometries

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume).

Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CR-structures and various types of generic distributions.

Authors: Hirschfeld, J.W.P, Thas, J.A.
Contains many applications to coding theory, algebraic geometry, incidence geometry, design theory, graph theory, and group theory
Provides detailed studies of quadrics, Hermitian varieties, Grassmann varieties, Veronese and Segre varieties
Unique being the only book of its kind

“I want to tell you what’s going on here. You don’t want to know… Is art just a substitute for what we’ve lost?” In his micro-opera Heretic, Richard Cameron-Wolfe’s enigmatic protagonist breaks the fourth wall, and in the process gives us a window into his artistic vision. Through exploration of dramatic and narrative subtlety in his micro-operas and text settings, expressive shadings of pitch in his use of microtonality, and finely etched treatment of timbre and gesture, Cameron-Wolfe reaches for the ineffable, something embedded in what we’ve “lost” or perhaps an essence of something that we can never possess. Throughout these chamber works, written over a thirty year period, we hear him calibrating his expression towards the mystery that lives between and beyond the sounds, obscuring the transparent surface in favor of the ambiguities of creative uncertainty.

Projective geometry, and the Cayley-Klein geometries embedded into it, were originated in the 19th century. It is one of the foundations of algebraic geometry and has many applications to differential geometry.

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume).

Automorphisms of a system survey its symmetry and appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, … and theoretical physics or chemistry. The main motivation of this book is to present a systemically introduction to automorphism groups on algebra, graphs, maps, i.e., graphs on surfaces and geometrical structures with applications.