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Difference between revisions of "Segre imbedding"

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<table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.R. Shafarevich,   "Basic algebraic geometry" , Springer (1977) (Translated from Russian)</TD></TR></table>
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<table><TR><TD valign="top">[1]</TD> <TD valign="top"> I.R. Shafarevich, "Basic algebraic geometry" , Springer (1977) (Translated from Russian) {{MR|0447223}} {{ZBL|0362.14001}} </TD></TR></table>
  
  
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> R. Hartshorne,   "Algebraic geometry" , Springer (1977) pp. Sect. IV.2</TD></TR></table>
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> R. Hartshorne, "Algebraic geometry" , Springer (1977) pp. Sect. IV.2 {{MR|0463157}} {{ZBL|0367.14001}} </TD></TR></table>

Revision as of 21:56, 30 March 2012

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=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