Talk:Main theorem of elimination theory
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Sketch of proof
[edit](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?
[edit]Why isn't this part of elimination theory? 31.50.156.122 (talk) 18:05, 3 July 2019 (UTC)
- Because the theorem can appear outside the context of elimination theory; namely in algebraic geometry. -- Taku (talk) 19:00, 3 July 2019 (UTC)