On finite affine line transitive planes

1965 ◽  
Vol 87 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Asher Wagner
Keyword(s):  
Finite Affine ◽  
Affine Line

scholarly journals Two algebraic deformations of a K3 surface

1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz
Keyword(s):  
Hyperelliptic Curve ◽  
Double Cover ◽  
Rational Curves ◽  
K3 Surface ◽  
Quartic Surface ◽  
Quadric Cone ◽  
Birational Model ◽  
Affine Line ◽  
Characteristic 2 ◽  
General Member

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.

Polycyclic-by-Finite Affine Group Schemes

1986 ◽  
Vol s3-52 (3) ◽  
pp. 495-516 ◽  
Author(s):  
W. W. Crawley-Boevey
Keyword(s):  
Affine Group ◽  
Group Schemes ◽  
Finite Affine

Order in Finite Affine Planes

1966 ◽  
Vol 9 (4) ◽  
pp. 407-411
Author(s):  
Mary Beattie ◽  
J.E. Marsden ◽  
R. W. Sharpe
Keyword(s):  
Affine Planes ◽  
Finite Affine

An ordered plane [1, p. 177 ff.] is a set of undefined entities called points, together with an undefined relation of intermediacy, satisfying the following axioms: (The symbol [ABC] means ″B is between A and C″.)

Equidistant Loci and the Minkowskian Geometries

1972 ◽  
Vol 24 (2) ◽  
pp. 312-327 ◽  
Author(s):  
B. B. Phadke
Keyword(s):  
Metric Spaces ◽  
Open Convex ◽  
Minkowskian Space ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Projective Metric ◽  
Affine Line ◽  
Finite Dimensional Banach Space ◽  
Homogeneous Norm ◽  
Symmetric Distance

The spaced of this paper is a metrization, with a not necessarily symmetric distance xy, of an open convex set D in the n-dimensional affine space An such that xy + yz = xz if and only if x, y, z lie on an affine line with y between x and z and such that all the balls px ≦ p are compact. These spaces are called straight desarguesian G-spaces or sometimes open projective metric spaces. The hyperbolic geometry is an example; a large variety of other examples is studied by contributors to Hilbert's problem IV. When D = An and all the affine translations are isometries for the metric xy, the space is called a Minkowskian space or sometimes a finite dimensional Banach space, the (not necessarily symmetric) distance of a Minkowskian space being a (positive homogeneous) norm. In this paper geometric conditions in terms of equidistant loci are given for the space R to be a Minkowskian space.

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