Talk:Main theorem of elimination theory

Latest comment: 5 years ago by TakuyaMurata in topic Move?

Sketch of proof

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(Put this to the article page, when it becomes complete.)

We need to show that   is closed for a ring R. Thus, let   be a closed subset, defined by a homogeneous ideal I of  . Let

 

where   is Then:

 .

Thus, it is enough to prove   is closed. Let M be the matrix whose entries are coefficients of monomials of degree d in   in

 

with homogeneous polynomials f in I and  . Then the number of columns of M, denoted by q, is the number of monomials of degree d in   (imagine a system of equations.) We allow M to have infinitely many rows.

Then   has rank   all the  -minors vanish at y.

Move?

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Why isn't this part of elimination theory? 31.50.156.122 (talk) 18:05, 3 July 2019 (UTC)Reply

Because the theorem can appear outside the context of elimination theory; namely in algebraic geometry. -- Taku (talk) 19:00, 3 July 2019 (UTC)Reply