Timeline for Motivation for birational geometry
Current License: CC BY-SA 4.0
10 events
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| S Mar 20 at 10:52 | history | suggested | littleman | CC BY-SA 4.0 |
Improved grammar in the statement of Lüroth's theorem
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| Mar 19 at 20:59 | review | Suggested edits | |||
| S Mar 20 at 10:52 | |||||
| Aug 2, 2021 at 0:03 | history | edited | Sándor Kovács | CC BY-SA 4.0 |
added 1 character in body
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| Jul 22, 2021 at 3:00 | history | edited | Sándor Kovács | CC BY-SA 4.0 |
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| Jul 22, 2021 at 2:58 | comment | added | Sándor Kovács | @roymend: 1) Who is that person "Kollar" you speak of? I never heard that name. 2) Theorem 30 in the linked article by Kollár is indeed about isomorphisms, but that says nothing about the importance of birational equivalence. | |
| Jul 22, 2021 at 2:55 | history | edited | Sándor Kovács | CC BY-SA 4.0 |
added 1399 characters in body
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| Jul 22, 2021 at 2:44 | comment | added | Sándor Kovács | @SamHopkins: I started answering in the comments, but it started to be pretty long, so I will do it within the original answer... | |
| Jul 21, 2021 at 11:56 | comment | added | roymend | I second @SamHopkins's question, and would really like to hear opinions on this. By the way, Kollar's article Sam linked to in a comment above, also seems to suggest that isomorphism is really the more valuable notion (theorem 30 there, which I found to be the most useful in terms of helping me understand what is geometric here, essentially says that for hypersurfaces, isomorphism is almost the same as projective equivalence. But then there's also theorem 36, which says a similar thing for birationality.) | |
| Jul 21, 2021 at 11:18 | comment | added | Sam Hopkins | In the answer to the version of the question on math.se, it is suggested that isomorphism is really what's significant, and birational equivalence is used as a step towards understanding isomorphism. Do you agree with that? Or would you say it's more like homeomorphism versus homotopy equivalence, where algebraic topologists have learned that the equivalence notion of real interest is not the naive one (perhaps because their techniques work best for the more sophisticated notion)? | |
| Jul 21, 2021 at 7:17 | history | answered | Sándor Kovács | CC BY-SA 4.0 |