Timeline for Lefschetz Theorem in Dolgachev's On automorphisms of Enriques Surfaces
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 8 at 23:51 | comment | added | Jason Starr | There is no theorem in mathematics that unravels because Dolgachev accidentally wrote the name "Lefschetz". | |
| Nov 8 at 22:37 | comment | added | user267839 | @JasonStarr: Because this may unravel a technique which up to wasn't familar to me, so I would like to understand how Dolgachev reasoned there, even though surely one could reason differently (eg exponential sequence) :) | |
| Nov 8 at 21:08 | comment | added | Jason Starr | If you understand a proof of each assertion, why does it matter what Dolgachev meant by “Lefschetz”? | |
| Nov 8 at 19:24 | comment | added | user267839 | ...this proof has a strange causal order... or I not understand it | |
| Nov 8 at 19:18 | comment | added | user267839 | @abx: hmm, what makes me a bit suspicious if that is really the reason why Dolgachev invoked Lefschetz is that one line before he already stated that $\operatorname{Pic}(F)=H^2(F,\Bbb Z)$ should hold due to Hodge decomposition. But that's also a strange reasoning, as a priori HD alone not gives this iso. What obvious that Dolgachev definitely not invokes there the exactness of LES of exponential sequence, as then in light of Enriquesness Lefschetz and HD would be redundant. | |
| Nov 8 at 18:52 | comment | added | abx | The Lefschetz result Dolgachev mentions is the isomorphism $\operatorname{Pic}(F)\cong H^2(F,\mathbb{Z}) $ when $H^{i}(F,\mathcal{O}_F)$ for $i=1,2$. | |
| Nov 8 at 18:42 | history | edited | user267839 | CC BY-SA 4.0 |
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| Nov 8 at 18:20 | history | edited | user267839 | CC BY-SA 4.0 |
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| Nov 8 at 18:05 | history | edited | user267839 | CC BY-SA 4.0 |
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| Nov 8 at 17:58 | history | edited | user267839 | CC BY-SA 4.0 |
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| Nov 8 at 17:53 | history | asked | user267839 | CC BY-SA 4.0 |