Timeline for Proving Hodge decomposition without using the theory of elliptic operators?
Current License: CC BY-SA 2.5
5 events
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| Jun 16, 2010 at 16:54 | comment | added | Konrad Voelkel | Just to point out the reference: Voisin mentions this in her Hodge Theory book, too, on page 206. She also mentions GAGA there but the complex conjugation property doesn't seem to follow from this (otherwise she would have mentioned that). | |
| Jun 16, 2010 at 8:08 | comment | added | Gunnar Þór Magnússon | Plus, to prove GAGA you need to know that the cohomology groups of a sheaf over a compact manifold are finite-dimensional. I've only seen this proved as an application of some hardcore functional analysis. | |
| Jun 15, 2010 at 16:52 | comment | added | Ravi Vakil | This is great, but hard, and unfortunately seems not an ideal alternate first route into Hodge theory. | |
| Jun 15, 2010 at 16:21 | comment | added | Boyarsky | But one has to prove that complex conjugation splits the Hodge filtration. Is that obvious just from knowing the dimensions add up correctly (which is what we'd get from GAGA)? | |
| Jun 15, 2010 at 16:10 | history | answered | Kevin H. Lin | CC BY-SA 2.5 |