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Hirzebruch–Milnor Classes and Steenbrink Spectra of Certain Projective Hypersurfaces

  • Laurentiu Maxim
  • Morihiko SaitoEmail author
  • Jörg Schürmann
Chapter
Part of the Progress in Mathematics book series (PM, volume 319)

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.

Keywords

Irreducible Component Complete Intersection Hyperplane Arrangement Smooth Projective Variety Mixed Hodge Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Laurentiu Maxim
    • 1
  • Morihiko Saito
    • 2
    Email author
  • Jörg Schürmann
    • 3
  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.RIMS Kyoto UniversityKyotoJapan
  3. 3.Mathematisches InstitutUniversität MünsterMünsterGermany

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