scholarly journals Hermitian Varieties in a Finite Projective Space PG(N, q2)

1966 ◽  
Vol 18 ◽  
pp. 1161-1182 ◽  
Author(s):  
R. C. Bose ◽  
I. M. Chakravarti
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Galois Field ◽  
Finite Projective Space ◽  
Finite Projective Spaces

The geometry of quadric varieties (hypersurfaces) in finite projective spaces of N dimensions has been studied by Primrose (12) and Ray-Chaudhuri (13). In this paper we study the geometry of another class of varieties, which we call Hermitian varieties and which have many properties analogous to quadrics. Hermitian varieties are defined only for finite projective spaces for which the ground (Galois field) GF(q2) has order q2, where q is the power of a prime. If h is any element of GF(q2), then = hq is defined to be conjugate to h.

Some Configurations in Finite Projective Spaces and Partially Balanced Incomplete Block Designs

1965 ◽  
Vol 17 ◽  
pp. 114-123 ◽  
Author(s):  
D. K. Ray-Chaudhuri
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Finite Projective Space ◽  
Block Designs ◽  
Incomplete Block ◽  
Finite Plane ◽  
Balanced Incomplete Block Designs ◽  
Pbib Design ◽  
Finite Projective Spaces ◽  
Balanced Incomplete Block

Using the methods developed in (2 and 3), in this paper we study some properties of the configuration of generators and points of a cone in an w-dimensional finite projective space. The configuration of secants and external points of a quadric in a finite plane of even characteristic is also studied. I t is shown that these configurations lead to several series of partially balanced incomplete block (PBIB) designs. PBIB designs are defined in Bose and Shimamoto (1). A PBIB design with m associate classes is an arrangement of v treatments in b blocks such that.

scholarly journals On homologies in finite combinatorial geometries

1975 ◽  
Vol 13 (1) ◽  
pp. 85-99 ◽  
Author(s):  
P.B. Kirkpatrick
Keyword(s):  
Projective Space ◽  
Automorphism Groups ◽  
Combinatorial Geometry ◽  
Projective Spaces ◽  
Finite Projective Space ◽  
Finite Projective Spaces ◽  
Trivial Element ◽  
Combinatorial Geometries

Any subset π* of the set of all planes through a line in a finite projective space PG(m, q) determines a subgeometry G(π*) of the combinatorial geometry associated with PG(m, q). In this paper the geometries G(π*) of rank greater than three in which every line contains at least four points, are characterized in terms of the existence of a certain set of automorphism groups Γ(C, X); where X is a copoint and C a point not in X, and each non-trivial element of Γ(C, X) fixes X and every copoint through C and fixes C and every point in X, but no other point; and where Γ(C, X) acts transitively on the points distinct from C and not in X of some line through C. As a corollary of the main theorem we obtain a characterization of the finite projective spaces PG(m, q) with m ≥ 3 and q ≥ 3.

scholarly journals On a certain homology of finite projective spaces

1983 ◽  
Vol 90 ◽  
pp. 57-62 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Finite Field ◽  
Projective Space ◽  
Linear Subspace ◽  
Projective Spaces ◽  
Finite Projective Spaces

We denote by Pn(q) the projective space of dimension n over a finite field GF(q) with q elements, and we mean by an i-flat a linear subspace of dimension i in Pn(q).

scholarly journals FINITE PROJECTIVE SPACES, GEOMETRIC SPREADS OF LINES AND MULTI-QUBITS

2012 ◽  
Vol 26 (27n28) ◽  
pp. 1243013
Author(s):  
METOD SANIGA
Keyword(s):  
Black Hole ◽  
Projective Space ◽  
Projective Spaces ◽  
Quadric Surface ◽  
Hermitian Variety ◽  
Finite Projective Spaces ◽  
New Perspective ◽  
Dimensional Projective Space ◽  
Nondegenerate Quadric

Given a (2N-1)-dimensional projective space over GF(2), PG (2N-1, 2), and its geometric spread of lines, there exists a remarkable mapping of this space onto PG (N-1, 4) where the lines of the spread correspond to the points and subspaces spanned by pairs of lines to the lines of PG (N-1, 4). Under such mapping, a nondegenerate quadric surface of the former space has for its image a nonsingular Hermitian variety in the latter space, this quadric being hyperbolic or elliptic in dependence on N being even or odd, respectively. We employ this property to show that generalized Pauli groups of N-qubits also form two distinct families according to the parity of N and to put the role of symmetric Pauli operators into a new perspective. The N = 4 case is taken to illustrate the issue, due to its link with the so-called black-hole/qubit correspondence.

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

scholarly journals Projective Reconstruction in Algebraic Vision

2019 ◽  
Vol 63 (3) ◽  
pp. 592-609
Author(s):  
Atsushi Ito ◽  
Makoto Miura ◽  
Kazushi Ueda
Keyword(s):  
Projective Space ◽  
Arbitrary Dimension ◽  
Projective Spaces ◽  
Rational Maps ◽  
Projective Reconstruction ◽  
Reconstruction Theorem

AbstractWe discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.

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