Timeline for Local representation of an analytic sets
Current License: CC BY-SA 2.5
2 events
| when toggle format | what | by | license | comment | |
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| May 12, 2010 at 14:44 | comment | added | BCnrd | Since c.i. implies Cohen-Macaulay, a non-normal surface which is regular in codimension 1 is not c.i. at the non-normal points (due to Serre's homological normality criterion). So scrunching up a smooth surface at a point does the job. For example, create a singularity at the origin in the affine plane: ${\rm{Spec}}(A)$ for $A \subset \mathbf{C}[x_1,x_2,x_3]$ the subring of $f$ satisfying $f \equiv f(0,0) \bmod (x_1,x_2,x_3)^2$ (i.e., $A = \mathbf{C}[x_i x_j]_ {1 \le i, j \le 3}$). | |
| May 12, 2010 at 9:51 | history | answered | vu viet | CC BY-SA 2.5 |