Search results for "Projective line"
showing 10 items of 14 documents
Quotients of the Dwork Pencil
2012
In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology.
Area minimizing projective planes on the projective space of dimension 3 with the Berger metric
2016
Abstract We show that, among the projective planes embedded into the real projective space R P 3 endowed with the Berger metric, those of least area are exactly the ones obtained by projection of the equatorial spheres of S 3 . This result generalizes a classical result for the projective spaces with the standard metric.
Partial spreads in finite projective spaces and partial designs
1975
A partial t-spread of a projective space P is a collection 5 p of t-dimensional subspaces of P of the same order with the property that any point of P is contained in at most one element of 50. A partial t-spread 5 p of P is said to be a t-spread if each point of P is contained in an element of 5P; a partial t-spread which is not a spread will be called strictly partial. Partial t-spreads are frequently used for constructions of affine planes, nets, and Sperner spaces (see for instance Bruck and Bose [5], Barlotti and Cofman [2]). The extension of nets to affine planes is related to the following problem: When can a partial t-spread 5 ~ of a projective space P be embedded into a larger part…
Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2
1996
Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.
Embedding finite linear spaces in projective planes, II
1987
Abstract It is shown that a finite linear space with maximal point degree n + 1 can be embedded in a projective plane of order n, provided that the line sizes are big enough.
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.
Una generalizzazione del birapporto sopra un anello
1990
We generalize to the case of the projective line over a (not necessarily commutative) ring the well-know theorem on the bijective maps preserving a given cross-ratio.
A Common Characterization of Finite Projective Spaces and Affine Planes
1981
Let S be a finite linear space for which there is a non-negative integer s such that for any two disjoint lines L, L' of S and any point p outside L and L' there are exactly s lines through p intersecting the two lines L and L'. We prove that one of the following possibilities occurs: (i) S is a generalized projective space, and if the dimension of S is at least 4, then any line of S has exactly two points. (ii) S is an affine plane, an affine plane with one improper point, or a punctured projective plane. (iii) S is the Fano-quasi -plane.
groups acting on the line and the circle with at most N fixed points
2022
A classical theme in dynamical systems is that the first fundamental information comes from the understanding of periodic orbits. When studying group actions, this means that we want to understand the fixed points of elements of the group, and a natural question that emerges from that is: Which groups of homeomorphisms can act on a 1-manifold having all non-trivial elements with at most N fixed points? Our main objective in this work is to approach that question and understand what properties can such dynamical hypothesis induces to the group.For the case N=0, a classical result from O. Hölder implies that such group of homeomorphisms acting on the line is always semi-conjugate to a subgrou…