Graphs of schemes associated to group actions

Kişisel A. U. Ö., Özkan E.

Hacettepe Journal of Mathematics and Statistics, cilt.53, sa.1, ss.145-154, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.15672/hujms.1206439
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.145-154
  • Anahtar Kelimeler: A-graph, Borel group action, Hilbert scheme
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Let X be a proper algebraic scheme over an algebraically closed field. We assume that a torus T acts on X such that the action has isolated fixed points. The T-graph of X can be defined using the fixed points and the one-dimensional orbits of the T-action. If the upper Borel subgroup of the general linear group with maximal torus T acts on X, then we can define a second graph associated to X, called the A-graph of X. We prove that the A-graph of X is connected if and only if X is connected. We use this result to give proof of Hartshorne’s theorem on the connectedness of the Hilbert scheme in the case of d points in ℙn.