  This paper proposes some material towards a theory of general toric varieties
without the assumption of normality. Their combinatorial description involves a
fan to which is attached a set of semigroups subjected to gluing-up conditions.
In particular it contains a combinatorial construction of the blowing up of a
sheaf of monomial ideals on a toric variety. In the second part it is shown
that over an algebraically closed base field of zero characteristic the
Semple-Nash modification of a general toric variety is isomorphic to the
blowing up of the sheaf of logarithmic jacobian ideals and that in any
characteristic this blowing-up is an isomorphism if and only if the toric
variety is non singular. In the second part we prove that orders on the lattice
of monomials (toric valuations) of maximal rank are uniformized by iterated
Sempla-Nash modifications.
