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BY 4.0 license Open Access Published by De Gruyter Open Access March 20, 2020

Another proof of the persistence of Serre symmetry in the Frölicher spectral sequence

Aleksandar Milivojević
From the journal Complex Manifolds


Serre’s duality theorem implies a symmetry between the Hodge numbers, hp,q = hnp,nq, on a compact complex n–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies dimE1p,q=dimE1np,nq for all p, q. Adapting an argument of Chern, Hirzebruch, and Serre [3] in an obvious way, in this short note we observe that this “Serre symmetry” dimEkp,q=dimEknp,nq holds on all subsequent pages of the spectral sequence as well. The argument shows that an analogous statement holds for the Frölicher spectral sequence of an almost complex structure on a nilpotent real Lie group as considered by Cirici and Wilson in [4].

MSC 2010: 32Q99; 53C56


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Received: 2020-01-20
Accepted: 2020-03-04
Published Online: 2020-03-20

© 2020 Aleksandar Milivojević, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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