Properties
The Segre variety is an example of a determinantal variety; it is the zero locus of the 2×2 minors of the matrix . That is, the Segre variety is the common zero locus of the quadratic polynomials
Here, is understood to be the natural coordinate on the image of the Segre map.
The fibers of the product are linear subspaces. That is, let
be the projection to the first factor; and likewise for the second factor. Then the image of the map
for a fixed point p is a linear subspace of the codomain.
Read more about this topic: Segre Embedding
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