Let $K$ be a field with infinitely many elements(I assume $\mathbb{C}$), $A = K[x_1,\dots,x_n]/I$ a finitely generated K–algebra. Then after a general linear coordinate change(I dont get this line), there exists a number $r\le n$, and an inclusion $K[x_1,\dots,x_r]\subseteq A$, such that A is a finitely generated $K[x_1,\dots,x_r]$–module. If moreover,$I\neq(0)$, then $r < n$. If $V = V (I)$, we also say that the projection on the first r coordinates $π : V \rightarrow K^r$ is a Noether normalization of $V$. Could any one explain me the geometric motivation behind the fact?I will be pleased if some one explain me the fact over $\mathbb{C}[x_1,x_2]$
Noether Normalization
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algebraic-geometry
commutative-algebra
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0No dear sir, then what are you recomending to study $f$irst? – 2012-05-19