4 problems

Let $k$ be a field, let $X\subset \mathbb{P}^n$ be a smooth hypersurface of degree at most $n$ with $X(k)\neq\emptyset$, and let $K_0(\operatorname{Var}/k)$ be the Grothendieck rin…

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…

Let $k$ be a $C_1$ field, and let an affine $k$-variety be defined by polynomial equations in $n$ variables whose sum of degrees is less than $n$. In the Grothendieck ring of varie…