Timeline for Where does the word "log" in log pair come from?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2022 at 22:36 | comment | added | Kim | Specializing to the case of MMP, why are log pairs the relevant thing to consider there? | |
| Apr 7, 2022 at 21:18 | comment | added | Ben Wieland | Oh, yeah, he seems to leave it to Hodge-Atiyah, who use them in the proof of lemma 17, but don't quite globalize them. | |
| Apr 7, 2022 at 18:29 | comment | added | Piotr Achinger | @BenWieland that's a great paper for sure, but logarithmic differential forms do not appear there, instead he uses forms with poles of arbitrary order. As far as I know, it was really Deligne's idea that the logarithmic de Rham complex is quasi-isomorphic to that. | |
| Apr 7, 2022 at 16:52 | comment | added | Ben Wieland | Grothendieck's letter to Atiyah is more leisurely than Hodge II, 3. | |
| Apr 7, 2022 at 15:50 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 16 characters in body
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| Apr 7, 2022 at 15:37 | comment | added | Vladimir Dotsenko | Indeed, one of the starting points is the fact that the cohomology of a complement of the normal crossing divisor can be computed via the sheaf of differential forms with logarithmic singularities along the divisor. This is discussed and used in a crucial way in Hodge II, Section 3. | |
| Apr 7, 2022 at 14:07 | comment | added | Wojowu | The general idea is that in log geometry goes around the idea of consider differential forms which aren't necessarily regular, bur have certain mild singularities, called logarithmic singularities, along $B$. The reason they are called so is because such forms are related to ones of the form $df/f$, which "morally" are just $d(\log f)$ (except we don't admit $\log f$ itself as a function, just this differential). | |
| Apr 7, 2022 at 13:18 | comment | added | Kim | I know some algebraic geometry on the level of Hartshorne. I don't know anything about log algebraic geometry, if that's what you're wondering. For what it's worth, I always favor longer and more detailed answers over shorter ones. | |
| Apr 7, 2022 at 12:19 | comment | added | Vladimir Dotsenko | It would help if you could clarify your background, the length of an answer would seriously depend on it. | |
| Apr 7, 2022 at 12:05 | history | asked | Kim | CC BY-SA 4.0 |