Suppose we know that the only associated points of Spec $\mathbb{C}[x,y]/ I$ were $[(y-x^2)]$, $[(x-1,y-1)]$ and $[(x-2,y-2)]$. Is there enough information to deduce if this scheme is reduced or not? I have been thinking about it, but I am confused. I would appreciate any comments/hints. Thank you!
2026-03-26 23:09:48.1774566588
Associated points of Spec $\mathbb{C}[x,y]/ I$
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A reduced ring has no embedded primes, see here: http://stacks.math.columbia.edu/tag/031O
But your ring has.