Titlebook: Some Properties of Differentiable Varieties and Transformations; With Special Referen Beniamino Segre Book 19571st edition Springer-Verlag

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Veronese Varieties and Modules of Algebraic Forms,a little separated from that exibited in the previous Parts, in view of the fresh methods which we employ. The local properties which we shall obtain can be used to establish a number of algebro-differential properties in the large. This fact we shall here demonstrate with particular reference to th

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Correspondences between Topological Varieties,e have obtained results of a local character and these fit into the global theory in a natural manner; also, the results now obtained should be compared with those of Parts Five and Six. However, the present global theory replies to questions and uses methods differing greatly from those which have

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Principal and Projective Curves of a Surface, and Some Applications,By applying several of the results of the preceding Part, we shall now introduce — on any non-developable surface of an ordinary space — some important ., the study of which will enable us to extend in certain directions the projective-differential theory of surfaces.

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Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folgehttp://image.papertrans.cn/s/image/871909.jpg

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Invariants of Contact and of Osculation. The Concept of Cross-ratio in Differential Geometry,c interpretation. This will have the effect of using in various ways the ., without leading however to proper extensions of such a notion to the differential field. We shall then consider a number of extensions of this type, methodically relating them to remarkable differential properties of appropriate varieties.

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Some Differential Properties in the Large of Algebraic Curves, their Intersections, and Self-correselements defined by intersections, or by fixed points of analytic or algebraic correspondences. Further, with regard to the above theory, intrinsic geometric interpretations will be introduced, which will imply geometric meanings for the differential invariants as they arise.