Show that the image of P n × P m under the Segre embedding ψ...

Ghillardi4Pi

Ghillardi4Pi

Answered

2022-12-04

Show that the image of P n × P m under the Segre embedding ψ is actually irreducible.

Answer & Explanation

Gwendolyn Case

Gwendolyn Case

Expert

2022-12-05Added 7 answers

So,show the preimage under the Segre map of an algebraic set is an algebraic subset of P n × P m .. If V were reducible, we could write V = V 1 V 2 ,, where V i V are closed. Then
P n × P m = S 1 ( V ) = S 1 ( V 1 ) S 1 ( V 2 )
where S 1 ( V i ) are closed. Picking x i V V i we have S 1 ( x i ) S 1 ( V i ) = so S 1 ( V i ) S 1 ( V ) is a strict inclusion, contradicting that P n × P m is irreducible.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?