  It is known that the weights of a complex weighted homogeneous polynomial $f$
with isolated singularity are analytic invariants of $(\mathbb C^d,f^{-1}(0))$.
When $d=2,3$ this result holds by assuming merely the topological type instead
of the analytic one.
  G. Fichou and T. Fukui recently proved the following real counterpart: the
blow-Nash type of a real singular non-degenerate convenient weighted
homogeneous polynomial in three variables determines its weights.
  The aim of this paper is to generalize the above-cited result with no
condition on the number of variables. We work with a characterization of the
blow-Nash equivalence called the arc-analytic equivalence. It is an equivalence
relation on Nash function germs with no continuous moduli which may be seen as
a semialgebraic version of the blow-analytic equivalence of T.-C. Kuo.
