Non-commutative varieties with curvature having bounded signature

  title={Non-commutative varieties with curvature having bounded signature},
  author={Harry Dym and J. William Helton and Scott A. McCullough},
  journal={arXiv: Functional Analysis},
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. 
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