  The signature(s) of the curvature of the zero set V of a free
(non-commutative) polynomial is defined as the number of positive and negative
eigenvalues of the non-commutative second fundamental form on V determined by
p. With some natural hypotheses, the degree of p is bounded in terms of the
signature. In particular, if one of the signatures is zero, then the degree of
p is at most two.
