Document Type

Article - preprint


Mathematics (HMC)

Publication Date



Motivated by scheme theory, we introduce strong nonnegativity on real varieties, which has the property that a sum of squares is strongly nonnegative. We show that this algebraic property is equivalent to nonnegativity for nonsingular real varieties. Moreover, for singular varieties, we reprove and generalize obstructions of Gouveia and Netzer to the convergence of the theta body hierarchy of convex bodies approximating the convex hull of a real variety.


Final published version can be found at:

Mohamed Omar, Brian Osserman, Strong nonnegativity and sums of squares on real varieties, Journal of Pure and Applied Algebra, Volume 217, Issue 5, May 2013, Pages 843-850, ISSN 0022-4049, (

Rights Information

© 2011 Mohamed Omar and Brian Osserman