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| -rw-r--r-- | controle-20230412.tex | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/controle-20230412.tex b/controle-20230412.tex index 9a12ee8..c7c55e6 100644 --- a/controle-20230412.tex +++ b/controle-20230412.tex @@ -583,10 +583,10 @@ means\footnote{Here $k^{\alg}$ denotes the algebraic closure of $k$, but feel free to assume that $k$ is algebraically closed ($k = k^{\alg}$) in this question.}: there is a Zariski closed set $Y$ in $\mathbb{P}^5$, defined over $k$ and contained in the Plücker quadric -$Q$ (defined by $\dagger$), such, for $w \in Q(k^{\alg})$, we have $w -\in Y(k^{\alg})$ if and only if $L_w \subseteq X(k^{\alg})$, where -$L_w$ denotes the line in $\mathbb{P}^3(k^{\alg})$ having Plücker -coordinates $w$.) +$Q$ (defined by $\dagger$), such that, for $w \in Q(k^{\alg})$, we +have $w \in Y(k^{\alg})$ if and only if $L_w \subseteq X(k^{\alg})$, +where $L_w$ denotes the line in $\mathbb{P}^3(k^{\alg})$ having +Plücker coordinates $w$.) The important part of this question is: how can we compute equations for $Y$ given the equation $h=0$ of $X$? |