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Suppose we have a smooth, complete toric varietiy $X_{\Sigma}$ of dimension $n$. Let $\sigma_k \in \Sigma(k)$ a smooth $k$-dimensional cone in $\Sigma$ and suppose we make the toric blow up at the ...

Let $\Pi$ denote the McMullen polytope algebra (over the field of rationals $\mathbb{Q}$) generated by convex polytopes with rational vertices in $\mathbb{R}^n$. For a simple polytope $P$ let us ...

Consider a convex rational polyhedral cone $C\subset\mathbb R^m$ with vertex at the origin. Let $X$ be the corresponding affine toric variety, i.e. $\mathbb C[X]=\mathbb C[\mathbb Z^m\cap C^\circ]$. ...

I was looking for such a result in the book by Cox, Little and Schenck but I'm not able to find a proper reference. All of the following requirements are tacitly assumed to be in the projective ...