Timeline for Compact and quasi-compact
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| May 29, 2019 at 18:28 | comment | added | user141225 | @PeteL.Clark I am not sure I understand. What algebraic geometers care about non-Moishezon complex manifolds (which are, in some sense, a majority)? Those that I have seen did not care but maybe my experience is limited. | |
| Mar 3, 2010 at 16:01 | comment | added | BCnrd | I'm doing both. As a contrast, algebraic geometers use the word "immersion" to mean (essentially) what differential geometers called "embedding", and in diff geom. "immersion" has a much broader meaning (for foliations, in Lie correspondence, etc.) which tends to not be relevant in A.G., hence no confusion (except for diff. geometers who need to read stuff in alg. geom.!). | |
| Mar 3, 2010 at 16:01 | comment | added | Pete L. Clark | The question contains a flawed premise -- algebraic geometers certainly do care about Hausdorff spaces, because they care about complex manifolds, Kahler metrics, Hodge theory, etc. Pointing out the flaw in the premise is an important part of the answer. Another (implicit, here, but explicit in other recent comments) premise is that algebraic geometers are the only ones who use quasi-compact and compact in this way. That's false: I do this, and I am a number theorist. | |
| Mar 3, 2010 at 15:49 | comment | added | Mariano Suárez-Álvarez | I guess you are commenting on the "they almost never deal with Hausdorff spaces" rather than answering his question? | |
| Mar 3, 2010 at 15:47 | comment | added | BCnrd | Now I have augmented my answer to clarify that I meant to also use the usual topology of the complex field. | |
| Mar 3, 2010 at 15:46 | history | edited | BCnrd | CC BY-SA 2.5 |
added 25 characters in body
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| Mar 3, 2010 at 15:26 | comment | added | Mariano Suárez-Álvarez | But that does not justify using a definition of compact which is different from everyone else, surely? | |
| Mar 3, 2010 at 15:23 | history | answered | BCnrd | CC BY-SA 2.5 |