Search results for "Real projective plane"
showing 6 items of 6 documents
A class of unitals of order q which can be embedded in two different planes of order q2
1987
By deriving the desarguesian plane of order q2 for every prime power q a unital of order q is constructed which can be embedded in both the Hall plane and the dual of the Hall plane of order q2 which are non-isomorphic projective planes. The representation of translation planes in the fourdimensional projective space of J. Andre and F. Buekenhouts construction of unitals in these planes are used. It is shown that the full automorphism groups of these unitals are just the collineation groups inherited from the classical unitals.
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.
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.
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.
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.
Maps to Projective Space
2000
One of the main goals of algebraic geometry is to understand the geometry of smooth projective varieties. For instance, given a smooth projective surface X, we can ask a host of questions whose answers might help illuminate its geometry. What kinds of curves does the surface contain? Is it covered by rational curves, that is, curves birationally equivalent to ℙ1? If not, how many rational curves does it contain, and how do they intersect each other? Or is it more natural to think of the surface as a family of elliptic curves (genus-1 Riemann surfaces) or as some other family? Is the surface isomorphic to ℙ2 or some other familiar variety on a dense set? What other surfaces are birationally …