  The higher Nash blowup of an algebraic variety replaces singular points with
limits of certain spaces carrying higher order data associated to the variety
at non-singular points. In the case of normal toric varieties we give a
combinatorial description of the higher Nash blowup in terms of a Gr\"obner
fan. This description will allow us to prove the analogue of Nobile's theorem
on the usual Nash blowup in this context. More precisely, we prove that for a
normal toric variety, the higher Nash blowup is an isomorphism if and only if
the variety is non-singular.

Algebraic Geometry