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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

-2 votes

A proof for a statement about polynomial automorphism

The very short proof I have is as follows. Suppose that $\Phi: k[x_1,...,x_n] \rightarrow k[y_1,...,y_n]$ is surjective then we have an isomorphism $k[x_1,...,x_n]/I \cong k[y_1,...,y_n]$ for some i …
mr.bigproblem's user avatar
2 votes
4 answers
2k views

A proof for a statement about polynomial automorphism

I already got a proof for the fact that if a polynomial map is surjective then it is also injective. However, I used the invariant dimension of a ring and I want a simpler proof. Bravo for any try. Fo …
mr.bigproblem's user avatar