Timeline for Non-Kahler manifolds and the dd^c-lemma
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 17, 2017 at 19:22 | comment | added | user21574 | Moreover to give reference to first comment of @JoséFigueroa-O'Farrill: see (5.23) Corollary. of the paper of Griffiths-Deligne et al link.springer.com/article/10.1007/BF01389853 | |
| Jul 21, 2017 at 4:13 | comment | added | user21574 | In previous comment, Bott-Chern and Aeppli cohomologies defined as $$H^{∙,∙}_{BC}(X):=\frac{ker∂∩ker\bar ∂}{im∂\bar ∂}$$ and $$H^{∙,∙}_A(X):=\frac{ker∂\bar ∂ }{im∂+im\bar ∂}$$. $H^k_{dR}(X,\mathbb C)$ is the de Rham cohomology. See Angella, DanieleTomassini, Adriano On the$ ∂\bar ∂$-lemma and Bott-Chern cohomology. Invent. Math. 192 (2013), no. 1, 71–81. | |
| Jul 21, 2017 at 4:04 | comment | added | user21574 | Let $X$ be a compact complex manifold. Then, for every $k\in\mathbb N$, the following equality holds $$∑_{p+q=k}(dim_{\mathbb C}H^{p,q}_{BC}(X)+dim_{\mathbb C}H^{p,q}_A(X))=2dim_{\mathbb C}H^k_{dR}(X,\mathbb C),$$ if and only if we have $\partial\bar\partial$-Lemma | |
| Apr 22, 2011 at 9:24 | vote | accept | Dmitry Egorov | ||
| Apr 21, 2011 at 21:19 | answer | added | Tony Pantev | timeline score: 12 | |
| Apr 21, 2011 at 18:43 | answer | added | YangMills | timeline score: 3 | |
| Apr 21, 2011 at 11:48 | comment | added | algori | complementing Jose's comment: ... or in fact anything bimeromorphic to a K\"ahler manifold, see Deligne, Griffiths, Morgan, Sullivan, Real homotopy type of K\"ahler manifolds. By the way, a explicit example of a Moishezon space is given in Appendix B of Hartshorne's Algebraic geometry. | |
| Apr 21, 2011 at 9:34 | comment | added | José Figueroa-O'Farrill | Any Moishezon manifold would do. So perhaps asking for explicit examples of Moishezon manifolds would answer your question. | |
| Apr 21, 2011 at 7:56 | answer | added | Craig | timeline score: 1 | |
| Apr 21, 2011 at 4:48 | history | asked | Dmitry Egorov | CC BY-SA 3.0 |