Let k be an algebraically closed field of characteristic 0 and let HG(d,N) be the open locus of the Hilbert scheme H(d,N) corresponding to Gorenstein subschemes of degree d
Nearby in the stack
in the projective N-space. We proved in a previous paper that
HG(d,N)
is irreducible for
d≤9
and
N≥1
. In the present paper we prove that also
HG(10,N)
is irreducible for each
N≥1
, giving also a complete description of its singular locus.