ON ENDOMORPHISMS OF ARRANGEMENT COMPLEMENTS

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HIZ A. S., Werner A.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.147, sa.7, ss.2797-2808, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 147 Sayı: 7
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1090/proc/14468
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2797-2808
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

Let Omega be the complement of a connected, essential hyperplane arrangement. We prove that every dominant endomorphism of Omega extends to an endomorphism of the tropical compactification X of Omega associated to the Bergman fan structure on the tropical variety trop(Omega). This generalizes a result in [Compos. Math. 149 (2013), pp. 1211-1224], which states that every automorphism of Drinfeld's half-space over a finite field Fq extends to an automorphism of the successive blow-up of projective space at all Fq-rational linear subspaces. This successive blow-up is in fact the minimal wonderful compactification by de Concini and Procesi, which coincides with X by results of Feichtner and Sturmfels. Whereas the proof in [Compos. Math. 149 (2013), pp. 1211-1224] is based on Berkovich analytic geometry over the trivially valued finite ground field, the generalization proved in the present paper relies on matroids and tropical geometry.