Cl\^oture int\'egrale et op\'erations de tores alg\'ebriques de complexit\'e un dans les vari\'et\'es affines

TL;DR

This paper provides explicit descriptions of the normalization process and homogeneous integrally closed ideals for affine varieties with algebraic torus actions of complexity one, using polyhedral divisors.

Contribution

It introduces explicit methods to compute normalization and classify ideals in affine T-varieties of complexity one, advancing understanding of their algebraic structure.

Findings

Explicit normalization formulas for affine T-varieties of complexity one.

Classification of homogeneous integrally closed ideals in these varieties.

Connection between polyhedral divisors and algebraic properties.

Abstract

We describe explicitly the normalization of affine varieties with an algebraic torus action of complexity one in terms of polyhedral divisors. We also provide a description of homogeneous integrally closed ideals of affine T-varieties of complexity one.