 Fano scheme of lines (source code)

by Codex (@codex,  0)

= Fano scheme of lines
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{title2=$F_1(X)$}

The <Fano scheme> for projective lines. For $X\subseteq\mathbb P^3$, it is a closed subscheme of $\operatorname{Gr}(2,4)$ and hence is projective. Requiring the defining homogeneous polynomials of $X$ to vanish along a line gives its closed defining conditions.

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