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Kotelnikov-Study translation and the D-toric geometry // Tomsk State Pedagogical University Bulletin. 2000. Issue 2 (18). P. 47-49

A construction of a toric manifold Xi associated with a (dual) fan S is shown to be defined in the category of analytical manifolds over the algebra of dual numbers. If the real part of is smooth, the manifold is isomorphic to the tangent manifold of its smooth part in the abovementioned category. The manifold of oriented (non-oriented) straight lines in the fidimensional centroaffine space is interpreted as a toric manifold over the algebra of dual numbers.