Abstract
Serre’s duality theorem implies a symmetry between the Hodge numbers, hp,q = hn−p,n−q, on a compact complex n–manifold. Equivalently, the first page of the associated Frölicher spectral sequence satisfies
References
[1] Angella, D., 2018. Hodge numbers of a hypothetical complex structure on S6. Differential Geometry and its Applications, 57, pp.105-120.10.1016/j.difgeo.2017.10.012Search in Google Scholar
[2] Bigalke, L. and Rollenske, S., 2007. The Frölicher spectral sequence can be arbitrarily non degenerate. arXiv preprint arXiv:0709.0481.10.1007/s00208-007-0206-zSearch in Google Scholar
[3] Chern, S.S., Hirzebruch, F. and Serre, J.P., 1957. On the index of a fibered manifold. Proceedings of the American Mathematical Society, pp.587-596.10.1090/S0002-9939-1957-0087943-0Search in Google Scholar
[4] Cirici, J. and Wilson, S.O., 2020. Dolbeault cohomology for almost complex manifolds. arXiv preprint arXiv:1809.01416.10.1016/j.aim.2021.107970Search in Google Scholar
[5] Cordero, L.A., Fernández, M. and Gray, A., 1991. The Frölicher spectral sequence for compact nilmanifolds. Illinois Journal of Mathematics, 35(1), pp.56-67.10.1215/ijm/1255987978Search in Google Scholar
[6] Deligne, P., Griffiths, P., Morgan, J. and Sullivan, D., 1975. Real homotopy theory of Kähler manifolds. Inventiones mathematicae, 29(3), pp.245-274.10.1007/BF01389853Search in Google Scholar
[7] Frölicher, A., 1955. Relations between the cohomology groups of Dolbeault and topological invariants. Proceedings of the National Academy of Sciences of the United States of America, 41(9), p.641.10.1073/pnas.41.9.641Search in Google Scholar PubMed PubMed Central
[8] McCleary, J., 2001. A user’s guide to spectral sequences (No. 58). Cambridge University Press.10.1017/CBO9780511626289Search in Google Scholar
[9] Popovici, D., Stelzig, J. and Ugarte, L., 2020. Some Aspects of Higher-Page Non-Kähler Hodge Theory. arXiv preprint arXiv:2001.02313.Search in Google Scholar
[10] Stelzig, J., 2018. On the structure of double complexes. arXiv preprint arXiv:1812.00865.Search in Google Scholar
© 2020 Aleksandar Milivojević, published by De Gruyter
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