2 problems

Let $f_1,\ldots,f_t$ be relatively prime real polynomials of positive degrees with respect to $x_{f+1},\ldots,x_r$, and let $x=(x_1,\ldots,x_f)$. Let $D(x)$ be a generalized discri…

Let $R$ be the real closed field under consideration, let $X$ and $Y$ be affine $R$-varieties, and let $pi:X\to Y$ be a morphism such that $pi_*\mathcal{O}_X$ is a free…