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Is there a theory of period map on non-Kähler manifolds that has Hodge decomposition? Any reference is helpful. Thank you.

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  • $\begingroup$ So I guess one way to parse this is if $f:X\to B$ is a proper holomorphic submersion with connected fibers, and the Frölicher spectral sequence degenerates for all fibers, is the induced map to the period domain holomorphic? I expect the answer is no. $\endgroup$
    – user145520
    Commented Aug 25, 2020 at 7:30
  • $\begingroup$ @user145520 Thank you for your comment. Is there any intuition or some ideas for you to believe it is wrong? $\endgroup$
    – Peter Liu
    Commented Aug 25, 2020 at 13:55
  • $\begingroup$ Have you checked Angella's book on non-Kähler geometry? He did some research on $\partial\bar\partial$ manifolds maybe provide some information which you need. $\endgroup$
    – Tom
    Commented Sep 5, 2020 at 12:10

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