Timeline for Holomorphic line bundles with torsion Chern class

Current License: CC BY-SA 4.0

12 events

when toggle format	what		by	license	comment
Jun 22, 2018 at 11:32	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 107 characters in body
Jun 22, 2018 at 11:27	comment	added	Francesco Polizzi		Deear Georges, you are right and right :-) Thank you very much for pointing out this, I will correct the answer.
Jun 22, 2018 at 9:29	comment	added	Georges Elencwajg		In their book Barth, Hulek, Peters and Van de Ven claim that indeed the image of $H^1(M,\mathbb Z)$ in $H^1(M,\mathcal O)$ is not a full lattice in the general case of a non-Kähler manifold. Here is the relevant page: books.google.fr/…
Jun 22, 2018 at 9:13	comment	added	Georges Elencwajg		Dear Francesco, here are the questions I ask myself: 1) We have $\dim H^1(M,\mathcal O)=h^{0,1.}$ (by Dolbeault) but you write $h^{1,0}$ for that number. The equality $h^{0,1.}=h^{1,0}$ requires a Kähler structure, I think. 2) Is the fact that $H^1(M, \, \mathbb{Z})$ is a full lattice in $H^1(M, , \mathcal{O}_M)$ not dependant on $M$ being Kähler?
Jun 22, 2018 at 8:26	comment	added	Francesco Polizzi		I added the assumption compact in the answer.
Jun 22, 2018 at 8:25	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 46 characters in body
Jun 21, 2018 at 20:49	comment	added	Francesco Polizzi		Dear Georges, I think that compact, complex manifold is enough. If not, where am I using the Kähler assumption?
Jun 21, 2018 at 20:43	comment	added	Georges Elencwajg		Dear Francesco, aren't you using some hypothesis on $M$ in your answer like, say, compact kähler ?
Jun 21, 2018 at 9:54	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 84 characters in body
Jun 21, 2018 at 9:36	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 20 characters in body
Jun 21, 2018 at 9:30	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 242 characters in body
Jun 21, 2018 at 9:24	history	answered	Francesco Polizzi	CC BY-SA 4.0