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Some Remarks on Hyperresolutions

  • J. H. M. SteenbrinkEmail author
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Abstract

We give an example of a cubical variety which does not admit a weak resolution in the sense of Guillén et al. (Hyperrésolutions Cubiques et Descente Cohomologique. Springer Lecture Notes in Mathematics, vol 1335. Springer, Berlin, 1988). We introduce the notion of a very weak resolution of a cubical variety, and we show that it always exists in characteristic zero. This suffices for the proof of the existence of cubical hyperresolutions.

Keywords

Cubical hyperresolution 

MSC classification:

14E15 

Notes

Acknowledgements

This note arose from a series of lectures entitled “Mixed Hodge theory of algebraic varieties” given by the author in the fall of 2014 at the Mathematical Sciences Center of Tsinghua University, Beijing, China. J.H.M. Steenbrink thanks this institute for its hospitality. Moreover he thanks Chris Peters for useful comments on an earlier draft of this paper.

References

  1. 1.
    Deligne, P.: Théorie de Hodge II. Publ. Math. I.H.E.S. 40, 5–58 (1971)Google Scholar
  2. 2.
    Deligne, P.: Théorie de Hodge III. Publ. Math. I.H.E.S. 44, 5–77 (1974)Google Scholar
  3. 3.
    Guillén, F., Navarro Aznar, V., Pascual-Gainza, P., Puerta, F.: Hyperrésolutions Cubiques et Descente Cohomologique. Springer Lecture Notes in Mathematics, vol. 1335. Springer, Berlin (1988)Google Scholar
  4. 4.
    Kollár, J., Kovács, S.: Singularities of the Minimal Model Program. Cambridge Tracts in Mathematics, vol. 200. Cambridge University Press, Cambridge (2013)Google Scholar
  5. 5.
    Peters, C.A.M., Steenbrink, J.H.M.: Mixed Hodge Structures. Ergebnisse der Mathematik, vol. 52. Springer, Berlin (2008)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.IMAPPRadboud University NijmegenNijmegenThe Netherlands
  2. 2.MSCTsinghua UniversityBeijingChina

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