Segre imbedding
From Encyclopedia of Mathematics
The imbedding 
of the product 
of projective spaces into the projective space 
, where 
. If 
, 
, and 
(
; 
) are homogeneous coordinates in 
, then the mapping is defined by the formula:
 |
where 
. The mapping 
is well-defined and is a closed imbedding. The image 
of a Segre imbedding is called a Segre variety. The case when 
has a simple geometrical meaning: 
is the non-singular quadric in 
with equation 
. The images 
and 
give two families of generating lines of the quadric.
The terminology is in honour of B. Segre.
References
| [1] | I.R. Shafarevich, "Basic algebraic geometry" , Springer (1977) (Translated from Russian) MR0447223 Zbl 0362.14001 |
Comments
References
| [a1] | R. Hartshorne, "Algebraic geometry" , Springer (1977) pp. Sect. IV.2 MR0463157 Zbl 0367.14001 |
How to Cite This Entry:
Segre imbedding. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Segre_imbedding&oldid=48643
Segre imbedding. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Segre_imbedding&oldid=48643
This article was adapted from an original article by Val.S. Kulikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article