Proceedings of the Edinburgh Mathematical Society · 1935 · 12 citations · 4 references
Natural SciencesMathematicsDescriptive GeometryGeometryTopologyAlgebraic GeometryAlgebraic TopologyComplex GeometryKnot TheoryLow-dimensional GeometryThree-dimensional GeometryAlgebraic SurfacesBirational GeometryComplex Algebraic VarietiesComplex SurfacesInvariantsSurface TopologySurfaces In Three-dimensional Geometry
The study of the topological properties of algebraic surfaces, considered as continua of four real dimensions, has thrown much light on the theory of the birational invariants of such loci. The results obtained for surfaces have been generalised to varieties of higher dimension by Hodge, and, particularly, by Lefschetz. Apart from this, little seems to be known about the general topological properties of algebraic loci of three (or more) dimensions, the detailed study of which seems to present considerable difficulty. In particular, apart from the general theorems of Lefschetz, nothing seems to be known about the cycles of three dimensions of an algebraic V 3 . The object of the present paper is to study these cycles on certain quite special V 3 , in the hope that some insight may be gained into the general theory.
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