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On the plane representation of the homaloidal surfaces which have a twisted cubic as multiple curve

Published online by Cambridge University Press:  20 January 2009

J. F. Tinto
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The most important application of the rational point transformations between two spaces lies in the construction of algebraical surfaces possessing singularities of various kinds and the investigation of their properties.

When a plane is transformed by such a transformation into a rational algebraical surface (homaloid) the geometry of the surface is immediately derivable from the geometry of the plane.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , February 1917 , pp. 2 - 16
Copyright
Copyright © Edinburgh Mathematical Society 1917

References

* Math. Ann., Bd. I. and II.

* A direct determination is given in §22.

* Noether (Math. Ann., Bd. III., p. 223), and Cayley (Crelle, Bd. 63). For a simple analytical proof see Proc. L. M. S., III., p. 14.

* There is a reduction of pn − 1 to be made from the number derived from the formula of §7. This arises from the presence of a degenerate curve in the pencil.