منابع مشابه
Smooth Projective Planes
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic to CP. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous to the theory ...
متن کاملProjective Planes in Algebraically
We investigate the combinatorial geometry obtained from algebraic closure over a fixed subfield in an algebraically closed field. The main result classifies the subgeometries which are isomorphic to projective planes. This is applied to give new examples of algebraic characteristic sets of matroids. The main technique used, which is motivated by classical projective geometry, is that a particul...
متن کاملExtending Partial Projective Planes
If a finite partial projective plane can be extended to a projective plane of order n, then it can be extended by a sequence of one line extensions. We describe necessary conditions for such an extension to exist, and restrictions which can be imposed on the intermediate sequence of extensions. This method can be used to attempt to construct a projective plane of non-prime-power order. 1. Parti...
متن کاملFake Projective Planes
1.1. A fake projective plane is a smooth compact complex surface which is not the complex projective plane but has the same Betti numbers as the complex projective plane. Such a surface is known to be projective algebraic and it is the quotient of the (open) unit ball B in C (B is the symmetric space of PU(2, 1)) by a torsion-free cocompact discrete subgroup of PU(2, 1) whose Euler-Poincaré cha...
متن کاملCorrespondences between projective planes
We characterize integral homology classes of the product of two projective planes which are representable by a subvariety.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1943
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1943-0008892-4