Abstract
We show that the Hirzebruch–Milnor class of a projective hypersurface, which gives the difference between the Hirzebruch class and the virtual one, can be calculated by using the Steenbrink spectra of local defining functions of the hypersurface if certain good conditions are satisfied, e.g., in the case of projective hyperplane arrangements, where we can give a more explicit formula. This is a natural continuation of our previous paper on the Hirzebruch–Milnor classes of complete intersections.
To the Memory of Friedrich Hirzebruch
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Acknowledgements
The first named author is partially supported by NSF-1304999. The second named author is partially supported by Kakenhi 24540039. The third named author is supported by the SFB 878 “groups, geometry and actions.”
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Maxim, L., Saito, M., Schürmann, J. (2016). Hirzebruch–Milnor Classes and Steenbrink Spectra of Certain Projective Hypersurfaces. In: Ballmann, W., Blohmann, C., Faltings, G., Teichner, P., Zagier, D. (eds) Arbeitstagung Bonn 2013. Progress in Mathematics, vol 319. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-43648-7_9
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