  Noether's problem asks whether, for a given field K and finite group G, the
fixed field L := K(x_h : h \in G)^G is a purely transcendental extension of K,
where G acts on the x_h by gx_h = x_gh. The field L is naturally the function
field of a quotient variety V := V (K,G). In analogy to the case of curves, we
define the gonality of V to be the minimal degree of a dominant rational map
from V to projective space, which, in a sense, measures the extent to which L
may fail to be purely transcendental over K. When G is abelian, we give bounds
for the gonality of V (K; G).

Algebraic Geometry