Paradan'S wall crossing formula for partition functions and Khovanski-Pukhlikov differential operator

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BOYSAL A., Vergne M.

Annales de l'Institut Fourier, cilt.59, sa.5, ss.1715-1752, 2009 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 5
  • Basım Tarihi: 2009
  • Doi Numarası: 10.5802/aif.2475
  • Dergi Adı: Annales de l'Institut Fourier
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1715-1752
  • Anahtar Kelimeler: Polytopes, Toric varieties
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Boğaziçi Üniversitesi Adresli: Evet

Özet

Let P(s) be a family of rational polytopes parametrized by inequations. It is known that the volume of P(s) is a locally polynomial function of the parameters. Similarly, the number of integral points in P(s) is a locally quasi-polynomial function of the parameters. Paul-Émile Paradan proved a jump formula for this function, when crossing a wall. In this article, we give an algebraic proof of this formula. Furthermore, we give a residue formula for the jump, which enables us to compute it.