Timeline for Union of varieties
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 2, 2017 at 5:20 | review | Close votes | |||
| Dec 4, 2017 at 11:43 | |||||
| Dec 1, 2017 at 22:03 | comment | added | Zach Teitler | Your question is whether $V(Q_1,\dotsc,Q_k)$ is an irreducible variety. Even if the $Q_i$ are each irreducible, the variety that they cut out is not necessarily irreducible. Jason's example is a reducible intersection of two irreducible quadric surfaces in $\mathbb{P}^3$. In the plane, the intersection of two irreducible conics is (generally) a set of $4$ points, which is reducible. | |
| Dec 1, 2017 at 21:14 | comment | added | Jason Starr | For $n$ equal to $3$, for $Q_1 = x_0x_3-x_1x_2$ and for $Q_2=x_0x_3+x_1x_2$, the common zero locus is contained in the union $\text{Zero}(x_0)\cup \text{Zero}(x_1)\cup\text{Zero}(x_2)\cup \text{Zero}(x_3)$, yet it is not contained in any one of these hyperplanes. | |
| Dec 1, 2017 at 21:05 | history | asked | Alexey Milovanov | CC BY-SA 3.0 |