Timeline for $\partial \bar{\partial}$ lemma for contractible domains

10 events

when toggle format	what		by	license	comment
Feb 7, 2017 at 14:09	history	edited	Francesco Polizzi	CC BY-SA 3.0	added 31 characters in body
Mar 26, 2011 at 2:10	vote	accept	Vamsi
Mar 25, 2011 at 18:10	history	edited	Gjergji Zaimi		edited tags
Mar 25, 2011 at 17:38	answer	added	Mohan Ramachandran		timeline score: 9
Mar 25, 2011 at 13:03	answer	added	David E Speyer		timeline score: 18
Mar 25, 2011 at 3:05	history	edited	Vamsi	CC BY-SA 2.5	added 11 characters in body; added 6 characters in body
Mar 25, 2011 at 0:59	comment	added	David E Speyer		Another nitpicky point: Take a holomorphic $(p-1, 0)$-form $\eta$ which isn't closed. Then $d \eta$ is a non-zero $d$-exact $(p,0)$ form, and it certainly isn't of the form $\partial \overline{\partial}$. So you'd better specify that both $p$ and $q \geq 1$. Again, in the compact Kahler case, all global holomorphic $(p-1,0)$ forms are closed, so this doesn't come up.
Mar 25, 2011 at 0:57	comment	added	David E Speyer		An obvious point: A nonzero $1$-form cannot be $\partial \overline{\partial}$-exact, so you want to specify that you are thinking of degrees $2$ and higher. Although this seems nitpicky, in the compact Kahler case, the $\partial \overline{\partial}$ lemma has no such hypothesis: A $d$-exact $(1,0)$ form or $(0,1)$ on a compact Kahler manifold must be $0$.
Mar 25, 2011 at 0:25	history	edited	Vamsi	CC BY-SA 2.5	deleted 3 characters in body
Mar 24, 2011 at 20:58	history	asked	Vamsi	CC BY-SA 2.5