For totally real varieties of codimension 3 (degree at least 6) or higher codimension with large degree, next-to-maximal quadratic persistence is equivalent to lying as a codimension-1 subvariety in a variety of minimal degree.
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On quadratic persistence and Pythagoras numbers of totally real projective varieties
For totally real varieties of codimension 3 (degree at least 6) or higher codimension with large degree, next-to-maximal quadratic persistence is equivalent to lying as a codimension-1 subvariety in a variety of minimal degree.