Sums of Squares on Projective Varieties

Chapter 7 starts with a discussion of varieties of minimal degree. The main result proved in this chapter states that an irreducible projective real variety X has minimal degree if, and only if, every non-negative quadratic form on X is a sum of squares of linear forms. Quantitative refinements are given as well. These results encompass several major classical theorems, among them the Hilbert 1888 theorems that were discussed in Chapter 2.