Clôture intégrale et opérations de tores algébriques de complexité un dans les variétés affines

Abstract

In this paper, we are interested in multigraded affine algebras of complexity 1. One of the main results gives a description of integrally closed homogeneous ideals in terms of polyhedral divisors introduced by Altmann−Hausen. Another result allows us to compute effectively the normalization of an affine variety with an algebraic torus action of complexity 1. We describe as well the integral closure of homogeneous ideals and exhibit new examples of normal homogeneous ideals.