Kalidor
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Trivial (!?) alg. geometry problem
Consider [tex]Y=Q_1,Q_2,\ldots,Q_r \subset \mathbb{A}^n[/tex], a finite set of [tex]r[/tex] different points. What are the generators of the ideal [tex]I(Y)[/tex]
Knowing that [tex]I(Q_i)=(X_1-Q_{i,1},\ldots,X_n-Q_{i,n})[/tex] and so on, my guess would be that the solution is something like
[tex](\prod_{k=1}^r f_{k,i}), 1 \leq i \leq n[/tex] with [tex]f_{k,i} \in I(Q_k)[/tex]
It seems kind of messed. Any ideas?
Homework Statement
Consider [tex]Y=Q_1,Q_2,\ldots,Q_r \subset \mathbb{A}^n[/tex], a finite set of [tex]r[/tex] different points. What are the generators of the ideal [tex]I(Y)[/tex]
The Attempt at a Solution
Knowing that [tex]I(Q_i)=(X_1-Q_{i,1},\ldots,X_n-Q_{i,n})[/tex] and so on, my guess would be that the solution is something like
[tex](\prod_{k=1}^r f_{k,i}), 1 \leq i \leq n[/tex] with [tex]f_{k,i} \in I(Q_k)[/tex]
It seems kind of messed. Any ideas?