TANNAKIAN CLASSIFICATION OF EQUIVARIANT PRINCIPAL BUNDLES ON TORIC VARIETIES

Biswas I., Dey A., Poddar M.

TRANSFORMATION GROUPS, cilt.25, sa.4, ss.1009-1035, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00031-020-09557-5
  • Dergi Adı: TRANSFORMATION GROUPS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1009-1035
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

LetXbe a complete toric variety equipped with the action of a torusT, andGa reductive algebraic group, defined over an algebraically closed fieldK. We introduce the notion of a compatible n-ary sumation -filtered algebra associated toX, generalizing the notion of a compatible n-ary sumation -filtered vector space due to Klyachko, where n-ary sumation denotes the fan ofX. We combine Klyachko's classification ofT-equivariant vector bundles onXwith Nori's Tannakian approach to principalG-bundles, to give an equivalence of categories betweenT-equivariant principalG-bundles onXand certain compatible n-ary sumation -filtered algebras associated toX, when the characteristic ofKis 0.