# ag.algebraic geometry – Degree of polynomials describing projection of algebraic set

Consider an algebraic subset $$Vsubseteq mathbb{R}^{n+1}$$ defined as the zero set of polynomials $${f_i}$$ and the projection map $$pi: mathbb{R}^{n+1}to mathbb{R}^n$$ deleting the last entry.

By the Tarski-Seidenberg theorem, the image $$pi(V)$$ is a semi-algebraic set. Is there a bound on the degree of the polynomials characterizing $$pi(V)$$ in terms of the degrees of the polynomials $$f_i$$?