Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 13
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Elias, Ben and Williamson, Geordie 2014. The Hodge theory of Soergel bimodules. Annals of Mathematics, p. 1089.


    Borisov, Lev A. and Paul Horja, R. 2013. On the better behaved version of the GKZ hypergeometric system. Mathematische Annalen, Vol. 357, Issue. 2, p. 585.


    Cattani, E. 2010. Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations. International Mathematics Research Notices,


    Dupont, Delphine 2010. Faisceaux pervers sur les variétés toriques lisses. Comptes Rendus Mathematique, Vol. 348, Issue. 15-16, p. 853.


    Fleming, Balin and Karu, Kalle 2010. Hard Lefschetz theorem for simple polytopes. Journal of Algebraic Combinatorics, Vol. 32, Issue. 2, p. 227.


    Au, Suanne Huang, Mu-wan and Walker, Mark E. 2009. The equivariant <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>K</mml:mi></mml:math>-theory of toric varieties. Journal of Pure and Applied Algebra, Vol. 213, Issue. 5, p. 840.


    Braden, Tom and Proudfoot, Nicholas 2009. The hypertoric intersection cohomology ring. Inventiones mathematicae, Vol. 177, Issue. 2, p. 337.


    Hower, Valerie 2008. Hodge spaces of real toric varieties. Collectanea mathematica, Vol. 59, Issue. 2, p. 215.


    Ehrenborg, Richard and Karu, Kalle 2007. Decomposition theorem for the cd-index of Gorenstein* posets. Journal of Algebraic Combinatorics, Vol. 26, Issue. 2, p. 225.


    Braden, Tom and Lunts, Valery A. 2006. Equivariant-constructible Koszul duality for dual toric varieties. Advances in Mathematics, Vol. 201, Issue. 2, p. 408.


    2006. An Introduction to Intersection Homology Theory, Second Edition.


    Karu, Kalle 2004. Hard Lefschetz theorem for nonrational polytopes. Inventiones mathematicae, Vol. 157, Issue. 2, p. 419.


    Stanley, Richard P. 2004. Recent developments in algebraic combinatorics. Israel Journal of Mathematics, Vol. 143, Issue. 1, p. 317.


    ×

Intersection Cohomology on Nonrational Polytopes[star ]

  • Paul Bressler (a1) and Valery A. Lunts (a2)
  • DOI: http://dx.doi.org/10.1023/A:1022232232018
  • Published online: 01 February 2003
Abstract

We consider a fan as a ringed space (with finitely many points). We develop the corresponding sheaf theory and functors, such as direct image Rπ* (π is a subdivision of a fan), Verdier duality, etc. The distinguished sheaf ${\cal L}_\Phi$, called the minimal sheaf plays the role of an equivariant intersection cohomology complex on the corresponding toric variety (which exists if Φ is rational). Using ${\cal L}_\Phi$ we define the intersection cohomology space IH(Φ). It is conjectured that a strictly convex piecewise linear function on Φ acts as a Lefschetz operator on IH(Φ). We show that this conjecture implies Stanley's conjecture on the unimodality of the generalized h-vector of a convex polytope.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Intersection Cohomology on Nonrational Polytopes[star ]
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Intersection Cohomology on Nonrational Polytopes[star ]
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Intersection Cohomology on Nonrational Polytopes[star ]
      Available formats
      ×
Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: