A friend of mine asked me a question that relates to algebraic geometry and convex programming.
The question was "What is the minimal size of a program that capture (the intended object is not necessarily one slice or a projection of the program (perhaps each slice captures at most one point of the variety) and the program could have arbitrary large but finite number of dimensions compared to the dimension of the space in which the variety at hand lives) the portion of a given algebraic curve presented by monomials that lies within a box around the origin?".
I am wondering can convex programs or quantified convex programs capture exactly one-dimensional curves or two dimensional surfaces etc. in affine spaces?
Or is there a characterization of what curves or surfaces can be captured?
Perhaps the question is trivial for well known and elementary reasons but in that case I just do not know.
