2 problems

Let $k$ be an algebraically closed field of characteristic $0$, and let $f$ be a homogeneous polynomial defining a hypersurface of degree $d$ in $\mathbb{P}^n$. A variety is…

Let $k$ be an algebraically closed field of characteristic $0$, and let $f_1,\ldots,f_l$ be homogeneous polynomials in $k[x_0,\ldots,x_n]$ satisfying … Let…