Non-commutative varieties with curvature having bounded signature (Q351750)

One of the aims of this paper is to introduce a notion of signature of the curvature of the zero set \(V(p)\) of a non-commutative polynomial \(p\) and to prove a lower bound in terms of the degree of the polynomial. It follows that, if the non-commutative variety \(V(p)\) has positive curvature, then the degree of \(p\) is at most two. A new version of a non-commutative analogue of the Hessian of \(p\) is also discussed.