Timeline for Cohen-Macaulay non-normal toric variety
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 17, 2016 at 7:51 | comment | added | Friedrich Knop | That's a good point. More generally, Serre's criterion says normal=R1+S2. Since CM implies S2 this means that $$\text{quasi-smooth toric}+\text{CM}+\text{smooth in codimension one}\Rightarrow\text{normal}$$ In other words, quasi-smooth non-normal toric varieties are almost never CM. | |
| Jun 16, 2016 at 21:32 | vote | accept | Joaquín Moraga | ||
| Jun 16, 2016 at 7:48 | answer | added | Friedrich Knop | timeline score: 3 | |
| Jun 16, 2016 at 7:46 | comment | added | Jason Starr | Cohen-Macaulay schemes are S2, hence satisfy the S2 extension property. So, beginning with $\mathbb{P}^n$, $n\geq 2$, "pinch" it infinitesimally at one point. The resulting scheme is not Cohen-Macaulay, even though the normalization morphism is universally bijective on points. | |
| Jun 16, 2016 at 0:11 | history | asked | Joaquín Moraga | CC BY-SA 3.0 |