Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added pointers to Fornaess-Stout on complex polydiscs here
I made some edits around the statement regarding good covers by Stein manifolds. Namely that these arenâ€™t good covers in the usual sense, rather acyclic in the sense of Dolbeault cohomology being trivial. This says nothing about e.g. $\mathbb{C}^*$-valued cohomology being trivial, hence one may not be able to trivialise for instance line bundles over such open covers.
Okay, so I had
Every complex manifold admits a good cover by Stein manifolds, in the sense that all finite non-empty intersections of the cover are Stein manifolds (e.g. Maddock, lemma 3.2.8 ). ).
and you have added
not in the sense that these intersections are contractible! Rather, all Dolbeault cohomology in positive degree vanishes.
A question:
what is the étale homotopy type of polydiscs in characteristic 0? Is it always trivial?
Yes, and some other pages where the notion appears, just to avoid people conflating the two concepts.
Just for the record, the other page is Stein manifold.
1 to 6 of 6