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Results tagged with complete-intersection
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user 14514
1
vote
If $X$ is an affine variety, is $X$ one component of a complete intersection with two?
I will consider the projective closure $X\subset\mathbb{P}^n$. Let say that $X$ is scheme theoretically defined by equations of degree $d_1\geq d_2\geq ... \geq d_m$. Then we can find $f_i \in H^0(X,\m …
- 8,998
1
vote
Accepted
Surface of type $(2,2)$ on the Segre cubic scroll $\mathbb{P}^1 \times \mathbb{P}^2 \subset ...
Here is another approach. Take a smooth surface $X$ of type $(d,2)$ in $S$. The general fiber of the projection $\pi:X\rightarrow \mathbb{P}^1$ is a smooth conic. So $X$ is rationally connected and si …
- 8,998
2
votes
Accepted
Linear sections of Segre varieties and rational normal scrolls
The scroll $S_{(1,k)}$ can be locally parametrized by the map
$$
\begin{array}{cccc}
\phi: & \mathbb{A}^1\times\mathbb{P}^1 & \longrightarrow & \mathbb{P}^{k+2}\\
& (u,[\alpha_0:\alpha_1]) & \mapsto …
- 8,998