Questions tagged [generic-points]

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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 $...
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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)...
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Point generation in polygon

I know about the Halton sequence. But so far I can’t find the formulas by which points are generated. Also worried is the question Halton sequence generates points only in the rectangle? Or can I ...
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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 ...
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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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Largeness, generic, random points

As presented in Oxtoby's book ( ), there are two notions of largeness for subspace $Y$ of a given space $X$: Topology: $X$ is a topological ...
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1 answer

Self-intersection and generic point

The Wikipedia entry on intersection theory contains the following statement: [for C a curve, on a surface] "the self-intersection points of C is the generic point of C, taken with multiplicity C · C."...
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Zero locus of a generic smooth section

Let $V$ be a smooth manifold, $E \rightarrow V$ a vector bundle over $V$ and $\Gamma$ be a finite group acting nontrivially on $V$ and $E$. Let $s \in C^\infty(E)$ be a generic $\Gamma$-equivariant ...
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6 answers

What are the most important instances of the "yoga of generic points"?

In algebraic geometry, an irreducible scheme has a point called "the generic point." The justification for this terminology is that under reasonable finiteness hypotheses, a property that is true at ...