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Using the language of polyhedral divisors and divisorial fans we describe invariant divisors on normal varieties X which admit an effective codimension one torus action.
Toroidal Embeddings I
G. Kempf, F. Knudsen, D. Mumford, and Saint-Donat. B · 1973
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Algebraic surfaces with k ∗ k^{*} -action
P. Orlik and P. Wagreich · 1977
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Classification of G G -varieties of complexity 1
D.A. Timashev · 1997
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Cartier divisors and geometry of normal G G -varieties
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Klaus Altmann and Jürgen Hausen · 2006
Later among the works it cites.
Gluing affine torus actions via divisorial fans
Klaus Altmann, Jürgen Hausen, and Hendrik Süß · 2008
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