Timeline for Weil Conjectures for Grassmannians
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| S Jan 3, 2017 at 9:15 | history | suggested | David Steinberg | CC BY-SA 3.0 |
fixed broken link
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| Jan 3, 2017 at 8:51 | review | Suggested edits | |||
| S Jan 3, 2017 at 9:15 | |||||
| Nov 24, 2009 at 19:34 | history | edited | Ilya Nikokoshev | CC BY-SA 2.5 |
linkifying
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| Nov 24, 2009 at 18:19 | comment | added | Mariano Suárez-Álvarez | @John: what Wikipedia means is that the simplest grassmanian which is not isomorphic to a projective space is $G(4,2)$, not that that is the simpler grassmanian which is not a projective variety (in which case we should correct it!) | |
| Nov 24, 2009 at 14:58 | comment | added | John McCarthy | Yes, yes, of course, the topology generated by the closed sets is equal to the closed sets, not something bigger. | |
| Nov 24, 2009 at 14:18 | comment | added | David E Speyer | What? Yes, this is precisely what Zariski closed means. (A homogenous ideal, when you are talking about projective space.) | |
| Nov 24, 2009 at 14:17 | comment | added | David E Speyer | It's not obvious, but it's true. Proof 1: Grassmannian's are proper, so the image of the Plucker embedding is closed. Proof 2: There are classic, explicit equations called the Plucker relations which cut out the Grassmannian. For a detailed and elementary proof that the Grassmannian is exactly the zeroes of the Plucker equations, see Ezra Miller and Bernd Sturmfels' book. | |
| Nov 24, 2009 at 14:16 | comment | added | John McCarthy | ok, yes, closed wrt the Zariski topology is not the same as the zeros of an ideal. | |
| Nov 24, 2009 at 14:14 | comment | added | David E Speyer | A projective variety is a closed subvariety of a projective space. | |
| Nov 24, 2009 at 14:13 | comment | added | John McCarthy | I know that you can embed a Grassmannian into projective space via the Plucker map, but it is not obvious to me that its image is the set of zeros of some ideal. | |
| Nov 24, 2009 at 14:10 | comment | added | John McCarthy | Why? Is it obvious? What does the comment in the wikipedi article The simplest "Grassmannian that is not a projective space is Gr2(4)" mean? | |
| Nov 24, 2009 at 14:07 | comment | added | Mariano Suárez-Álvarez | @John: What do you mean? The usual Grassmanians (subspaces of a fixed dimension in a vector space of a given dimension) is always projective. | |
| Nov 24, 2009 at 14:05 | comment | added | John McCarthy | A question that just occurred to me: There exist Grassamnians that are not projective varieties? if so, does the formulation of the Weil conjectures still trouble free? | |
| Nov 24, 2009 at 14:03 | vote | accept | John McCarthy | ||
| Nov 24, 2009 at 13:59 | history | answered | Dror Speiser | CC BY-SA 2.5 |