Some Remarks on Hyperresolutions

  • J. H. M. SteenbrinkEmail author


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.


Cubical hyperresolution 

MSC classification:




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.


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© Springer International Publishing AG 2017

Authors and Affiliations

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

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