scholarly journals On the Hilbert scheme of curves in higher-dimensional projective space

1996 ◽  
Vol 90 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Barbara Fantechi ◽  
Rita Pardini
Keyword(s):  
Projective Space ◽  
Hilbert Scheme ◽  
Higher Dimensional ◽  
Dimensional Projective Space

scholarly journals Singularities of Projective Embedding (Points of order n on an Elliptic Curve)

1972 ◽  
Vol 45 ◽  
pp. 97-107 ◽  
Author(s):  
Akikuni Kato
Keyword(s):  
Projective Space ◽  
Elliptic Curve ◽  
Vector Bundles ◽  
Neutral Element ◽  
Projective Embedding ◽  
Dual Formulation ◽  
Higher Dimensional ◽  
Dimensional Projective Space ◽  
Dimension One ◽  
Principal Parts

In the Plücker formula for a curve embedded in a higher dimensional projective space, one encounters the notion of stationary point (cf, [B], [W]). W. F. Pohl gave new view point about it in terms of vector bundles and he defined “the singularities of embedding” (cf. [P]). At first, we shall give dual formulation of Pohl’s one by means of the sheaf of principal parts of order n, and next we shall prove the following: If an elliptic curve is embedded in (n — l)-dimensional projective space as a curve of degree n, singularities of projective embedding of order n — 1 are exactly the points of order n with suitable choice of a neutral element on the curve which is an abelian variety of dimension one. The proof is given by making use of the relation between and Schwarzenberger’s secant bundle which we shall also give.

Thomas Gerald Room, 10 November 1902 - 2 April 1986

1987 ◽  
Vol 33 ◽  
pp. 573-601
Keyword(s):  
Projective Space ◽  
Mathematics Teachers ◽  
New South ◽  
New South Wales ◽  
South Wales ◽  
Higher Dimensional ◽  
Dimensional Projective Space ◽  
The University ◽  
Insight Into ◽  
Profound Insight

Thomas Gerald Room, Professor of Mathematics in the University of Sydney from 1935 until his retirement in 1968, died at his home near Sydney on 2 April 1986, at the age of 83. Born and educated in England, he came to Sydney in his early thirties and made it his adopted home. He was a classical geometer with unusual gifts of intuition and combinatorial skill, who will be particularly remembered for his profound insight into configurations in higher dimensional projective space. He and his slightly older contemporary, T. M. Cherry, were the elder statesmen of Australian mathematics in their time. He exerted enormous influence on the course of mathematics in New South Wales at both school and university levels and will be remembered by mathematicians, mathematics teachers and generations of students.

Transformations depending on sets of associated points

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Three Dimensional ◽  
Cubic Curves ◽  
Birational Transformations ◽  
Quadric Surfaces ◽  
Base Points ◽  
Dimensional Projective Space ◽  
Quartic Curves

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).

The geometry and algebra of the representations of the Lorentz group

1968 ◽  
Vol 303 (1474) ◽  
pp. 381-396 ◽  
Keyword(s):  
Projective Space ◽  
Lorentz Group ◽  
Point Of View ◽  
Normal Curve ◽  
Geometrical Representation ◽  
Spinor Space ◽  
Dimensional Projective Space ◽  
And Algebra ◽  
Rational Normal Curve ◽  
Formal Point

In this paper a (2j + l)-spinor analysis is developed along the lines of the 2-spinor and 3-spinor ones. We define generalized connecting quantities A μv (j) which transform like (j, 0) ⊗ (j -1, 0) in spinor space and like second rank tensors under transformations in space-time. The general properties of the A uv are investigated together with algebraic relations involving the Lorentz group generators, J μv . The connexion with 3j symbols is discussed. From a purely formal point of view we introduce a geometrical representation of a (2j +1)-spinor as a point in a 2j dimensional projective space. Then, for example, the charge con­jugate of a (2j + l)-spinor is just the polar of the corresponding point with respect to a certain rational, normal curve in the projective space. It is suggested that this representation will prove useful.

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