Questions tagged [generic-points]
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10 questions
2 votes
0 answers
127 views
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 $d=\dim(\Sigma)$ ...
- 539
1 vote
0 answers
78 views
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 $...
- 263
1 vote
0 answers
83 views
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)...
- 545
0 votes
1 answer
230 views
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 ...
- 103
0 votes
0 answers
54 views
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 ...
- 461
3 votes
0 answers
304 views
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 ...
- 31
2 votes
1 answer
181 views
Largeness, generic, random points
As presented in Oxtoby's book ( http://link.springer.com/book/10.1007%2F978-1-4615-9964-7 ), there are two notions of largeness for subspace $Y$ of a given space $X$: Topology: $X$ is a topological ...
- 370
2 votes
1 answer
401 views
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."...
- 3,311
0 votes
1 answer
1k views
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 ...
- 1,977
21 votes
6 answers
4k views
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 ...
- 24.6k