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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 $\mathbb{P}^2_K$ ...
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Varieties with few trisecant lines

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 $i$....
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Varieties with few trisecant lines

A consequence of Gruson-Peskine $k$-secant lemma is the following : if $2N -3n-1>0$ then the trisecants of $X$ do not fill the ambiant space. In particular, if you know that the secant variety of $...
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Varieties with few trisecant lines

You can have a look at Ingrid Bauer's paper Bauer, I., The classification of surfaces in $\mathbb{P}^5$ having few trisecants, Rend. Semin. Mat., Torino 56, No. 1, 1-20 (1998). ZBL0965.14029. It turns ...
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1 vote
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Birational morphisms from DM stacks to their coarse moduli spaces

Yes. For each nontrivial element $g\in G$, the fixed points form a closed set, which must not contain the whole space as then $g$ would act trivially (by reducedness). The complementary open set thus ...
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