Fermat hypersurface diagonal symmetry
= Fermat hypersurface diagonal symmetry
{c}
The Fermat hypersurface $z_0^d+\cdots+z_n^d=0$ is preserved by multiplying each coordinate by a $d$th root of unity. Projective scalar multiplication is trivial, so the effective diagonal group is
$$
(\mathbb Z/d\mathbb Z)^{n+1}/\langle(1,\ldots,1)\rangle\cong(\mathbb Z/d\mathbb Z)^n.
$$
These transformations preserve the <Fubini-Study form>.