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Segre imbedding

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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)


Comments

References

[a1] R. Hartshorne, "Algebraic geometry" , Springer (1977) pp. Sect. IV.2
How to Cite This Entry:
Segre imbedding. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Segre_imbedding&oldid=23973
This article was adapted from an original article by Val.S. Kulikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article