Timeline for How to compute the dimension of a linear system on $\mathbb{P}^n$
Current License: CC BY-SA 2.5
6 events
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| Mar 23, 2011 at 13:36 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 15 characters in body; edited title
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| Mar 23, 2011 at 13:34 | answer | added | Francesco Polizzi | timeline score: 2 | |
| Feb 4, 2010 at 18:38 | comment | added | algori | Here is an answer assuming "passes through" means "contains": to each projective variety there corresponds a homogeneous ideal (it is formed by all polynomials that are zero at each point of the subvariety) and the dimension of the linear system of quadrics containing the subvariety is the degree 2 part of the ideal. In the above example (complete intersection of 4 quadrics) we get 4. | |
| Feb 4, 2010 at 18:31 | comment | added | algori | Charles -- probably this means "contains" because otherwise we don't get a linear system in general. | |
| Feb 4, 2010 at 15:02 | comment | added | Charles Siegel | By "pass through" do you mean "contains" or "intersects"? I usually only see that phrasing when talking about individual points. | |
| Feb 4, 2010 at 13:45 | history | asked | Guangbo Xu | CC BY-SA 2.5 |