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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 EMAIL logo
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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