Questions tagged [generic-points]

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Generic points of algebraic stacks

I am aware that this is not a esearch question, but I don't know where else to ask. I have come across the fact that the stack of bundles of rank r and degree d over a curve of genus g with a ...
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Geometric generic point of a complete linear system

In the following context: Let $S$ be a connected smooth projective surface over $\mathbb{C}$, and let $\Sigma$ be the complete linear system of a very ample divisor $D$ on $S$. Let $d=\dim(\Sigma)$ ...
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dimension of fibre of a generic point in an intersection of two sets

Let $M_m := (f_1, \cdots, f_m )$ be an algebraic map from $\mathbb{R}^n$ to $\mathbb{R}^m$ and $f_1^2,...,f_m^2$ are homogeneous polynomials of the same degree in $Q[x_1,...,x_n]$ . Similarly define $...
Pew's user avatar
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Why are trivalent/cubic graphs 'generic' in surfaces?

I've seen some statements that trivalent graphs in a surface are 'generic'. See for example the Wiki entry on cubic graphs. I'm wondering how this could be rephrased. Here are some (somewhat imprecise)...
Joe's user avatar
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Condition on the point cloud matrix making the points "generic" in the uniform sense

For a matrix $X\in\mathbb{R}^{d\times n}$, what condition can I impose on $X$ to make the collection of its columns generic in the sense that they look like the result of uniformly sampling a convex ...
Min Wu's user avatar
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