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J1U
  • Member for 6 years, 2 months
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Group action on affine variety induces faithful action on tangent space
This is just a gut feeling, but I think one must have the decomposition $A/m^k=V\oplus V^2 \oplus \cdots \oplus V^{k-1}$.
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The left exactness of conormal sequence when $X$ is singular
@DevlinMallory But here $I$ is $(x,y)$. I am considering the case that the ambient space itself is singular, $X=\mathrm{Spec} k[x,y,z]/(xz-y^2)$, and $Z$ is the zero set of $(x,y)$.
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The left exactness of conormal sequence when $X$ is singular
@DevlinMallory But isn't $x\in I/I^2$ in the second example a torsion since $zx=y^2=0$, viewed as $k[z]$-module? What am I missing?
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