Search results for "Projective plane"

Graphs of stable maps from closed surfaces to the projective plane

2018

Abstract We describe how to attach a weighted graph to each stable map from closed surfaces to projective plane and prove that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane.

Projective mappings between projective lattice geometries

1995

The concept of projective lattice geometry generalizes the classical synthetic concept of projective geometry, including projective geometry of modules.

On the level of projective spaces

1987

An algebraic loop theorem and the decomposition of PD 3 -pairs

2006

Projective spaces on partially ordered sets and Desargues' postulate

1991

We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.

Embedding Locally Projective Planar Spaces Into Projective Spaces

1988

We shall show that a 3-dimensional locally projective planar space of finite order n can be embedded into a 3-dimensional projective space of order n, if it has at least n 3 points.

Embedding linear spaces with two line degrees in finite projective planes

1986

In this paper we shall classify all finite linear spaces with line degrees n and n-k having at most n2+n+1 lines. As a consequence of this classification it follows: If n is large compared with k, then any such linear space can be embedded in a projective plane of order n−1 or n.

On n–Fold Blocking Sets

1986

An n-fold blocking set is a set of n-disjoint blocking sets. We shall prove upper and lower bounds for the number of components in an n-fold blocking set in projective and affine spaces.

Mapping the geometry of the F(4) group.

2007

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2=F4/Spin(9), the octonionic projective plane, these results are a prerequisi…

Counting and equidistribution in Heisenberg groups

2014

We strongly develop the relationship between complex hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on complex hyperbolic spaces, especially in dimension $2$. We prove a Mertens' formula for the integer points over a quadratic imaginary number fields $K$ in the light cone of Hermitian forms, as well as an equidistribution theorem of the set of rational points over $K$ in Heisenberg groups. We give a counting formula for the cubic points over $K$ in the complex projective plane whose Galois conjugates are orthogonal and isotropic for a given Hermitian form over $K$, and a counting and equidistribution result for …