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Let $X$ be an affine toric variety defined over an algebraically closed field $k$ of characteristic zero. I am trying to use Bloch’s Riemann-Roch Theorem for quasi-projective algebraic schemes in his ...

Let $k$ be an algebraically closed field and let $\sigma$ be a 3-dimensional simplicial cone in $\mathbb{R}^3$.Let $X$ be the affine toric variety over $k$ associated to the cone $\sigma$, i.e. set $X$...

Let $k$ be an algebraically closed field of characteristic zero. Let $m$ be a positive integer and let $X$ be the weighted projective space $\mathbb{P}(1,1,m)$ over the field $k$.I am trying to ...

Let $k$ be an algebraically closed field of characteristic zero. Let $\sigma$ be the cone in $\mathbb{R}^3$ generated by $e_1,2e_1+e_2,e_1+2e_2+3e_3$. Then it is easy to check that $\sigma$ is a 3-...

Let $k$ be an algebraically closed field of characteristic zero. Let $\Sigma$ be the fan in $\mathbb{R}^2$ consisting of three cones, cone generated by $e_1,e_2$,cone generated by $e_2,-e_1-2e_2$ and ...

Let $k$ be an algebraically closed field of characteristic zero. Let $\sigma_0$ be the cone in $\mathbb{R}^2$ generated by $e_1,e_2$.And let $\sigma_1$ be the cone in $\mathbb{R}^2$ generated by $e_2,-...