Timeline for Surjectivity of $H^2(X,\mathbb C)\to H^2(X,\mathcal O)$

5 events

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Oct 4, 2022 at 9:54	comment	added	Tom		I still have 2 questions: (i) Is your condition (2) necessary to ensure the map $f$ being surjective? which seems contradict to Prof Arapura's comment. (ii) Your condition (1): $E_1^{p,q}=E_{\infty}^{p,q}$, which means $H^{p,q}_{\bar\partial}(X)=\frac{F^pH^{p+q} (X)}{F^{p+1}H^{p+q}(X)}$, where $F^pH^{p+q}:=\frac{F^pA^{p+q}\cap\text{ker }d}{F^pA^{p+q}\cap\text{im }d}$, but both of these two groups are not the subspace of $H^{p+q}(X)$ represented by $d$-closed forms, which may be seemed as $\frac{A^{p,q}\cap\text{ker }d}{A^{p,q}\cap\text{im }d}$？ Can you elaborate it a bit?
Oct 3, 2022 at 13:53	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 4 characters in body
Oct 3, 2022 at 13:13	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 2 characters in body
Oct 3, 2022 at 13:05	history	edited	Francesco Polizzi	CC BY-SA 4.0	added 2 characters in body
Oct 3, 2022 at 12:54	history	answered	Francesco Polizzi	CC BY-SA 4.0