Given a cohomology class there is a smooth submanifold Poincaré dual to . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in . This note summarizes some results on the question: how does the divisibility of restrict the dual submanifolds in this class ? A formula for signatures associated with a -fold ramified cover of branched along is given and a proof is included in case .
Étant donné une classe de cohomologie , il existe une sous-variété duale à dans le sens de Poincaré. Il existe un ensemble de tels plongements qui est caractérisé par des propriétés topologiques, que les hypersurfaces algébriques de vérifient. Cet exposé résume quelques résultats sur la question : comment la divisibilité de limite-t-elle les sous-variétés duales, , dans cet ensemble ? Et nous donnons une formule pour la signature associée à un revêtement d’ordre sur , ramifiée sur ; nous le démontrons dans le cas où .
@article{AIF_1973__23_2_229_0, author = {Wood, J. and Thomas, Emery}, title = {On signatures associated with ramified coverings and embedding problems}, journal = {Annales de l'Institut Fourier}, pages = {229--235}, publisher = {Imprimerie Durand}, address = {28 - Luisant}, volume = {23}, number = {2}, year = {1973}, doi = {10.5802/aif.470}, zbl = {0262.57012}, mrnumber = {49 #3964}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.470/} }
TY - JOUR TI - On signatures associated with ramified coverings and embedding problems JO - Annales de l'Institut Fourier PY - 1973 DA - 1973/// SP - 229 EP - 235 VL - 23 IS - 2 PB - Imprimerie Durand PP - 28 - Luisant UR - https://aif.centre-mersenne.org/articles/10.5802/aif.470/ UR - https://zbmath.org/?q=an%3A0262.57012 UR - https://www.ams.org/mathscinet-getitem?mr=49 #3964 UR - https://doi.org/10.5802/aif.470 DO - 10.5802/aif.470 LA - en ID - AIF_1973__23_2_229_0 ER -
Wood, J.; Thomas, Emery. On signatures associated with ramified coverings and embedding problems. Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 229-235. doi : 10.5802/aif.470. https://aif.centre-mersenne.org/articles/10.5802/aif.470/
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