# Tag Info

Accepted

### Noether–Enriques using Tsen's lemma

I will assume that $X$ is proper. Then the generic fiber is a smooth projective curve of genus $0$ over the function field $K = k(Z)$ but any such curve can be embedded as a conic in $\mathbb{P}^2_K$ ...
• 1,918
Assume that $X$ is set theoretically defined by quadrics: $X = Q_1\cap\dots\cap Q_r$. If $L$ is a line trisecant to $X$ then $L$ is trisecant to $Q_i$ for all $i$ and hence $L\subset Q_i$ for all $i$....