Timeline for Cubic 3-fold singular along a curve
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2019 at 19:56 | comment | added | abx | I think so. Let $C$ be a general complete intersection of 3 quadrics in $\mathbb{P}^4$, given by $P=Q=R=0$. The quartic threefold $X$ defined by $P^2+Q^2+R^2=0$ has $\operatorname{Sing}(X)=C $. Now I don't know what you call "$A_1$-singularities along $C$", but the singularities of $X$ along $C$ are as nice as they can be. | |
| Mar 4, 2019 at 18:55 | comment | added | user56259 | You are right. Thank you. Do you know if there exists a quartic 3-fold with this property? | |
| Mar 4, 2019 at 18:54 | history | edited | user56259 | CC BY-SA 4.0 |
added 11 characters in body
|
| Mar 4, 2019 at 18:05 | comment | added | abx | No. If $\operatorname{Sing}(X) =C$ every bisecant line to $C$ must be contained in $X$. This implies easily that $C$ is rational. | |
| Mar 4, 2019 at 17:45 | history | asked | user56259 | CC BY-SA 4.0 |