Polyhedral divisors and torus actions of complexity one over arbitrary fields

• Kevin Langlois ^[1]
  1. [1] Université Grenoble I, France
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 2015-2045
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.07.021
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• Resumen

  • We show that the presentation of affine TT-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra associated with a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine G-varieties of complexity one over a field, where G is a (not necessarily split) torus, by using elementary facts on Galois descent. This class of affine G-varieties is described via a new combinatorial object, which we call (Galois) invariant polyhedral divisor.