Abstract
I investigate the degeneration behavior of the Frölicher spectral sequence of a submersive, but generally nonproper, morphism g: Y → S of complex spaces. The morphism g is assumed to come about as the restriction of a proper morphism of complex spaces f: X → S to an open complex subspace of X. The morphism f is assumed to be flat for the most part. Moreover, the fibers of f are assumed to be of Kähler type. The degeneration criteria for the Frölicher spectral sequence of g are expressed in terms of the codimension of the complement X ∖ Y inside the fibers of f. My results are relative analogues of a theorem of T. Ohsawa (Publ. Res. Inst. Math. Sci. 23(4), 613–625, 1987. doi:10.2977/prims/1195176250).
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Notes
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Here, a module is pair (A,M) consisting of a ring A and a module M over A.
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Kirschner, T. (2015). Degeneration of the Frölicher Spectral Sequence. In: Period Mappings with Applications to Symplectic Complex Spaces. Lecture Notes in Mathematics, vol 2140. Springer, Cham. https://doi.org/10.1007/978-3-319-17521-8_2
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