3 problems

Let $\Delta$ be a complete fan of dimension $n$, and let ${\mathcal A}(B\Delta)$ be its associated graded algebra with elements $L_i\in {\mathcal A}(B\Delta)$ of degree $e_i$, for…

Filtration monotonicity under refinement. One has

For each vertex $v$ of the exchange graph, let $\operatorname{Cone}(v)$ be the cone in $V^*$ spanned by the weights $\mathbf g(x^v_e)$ for $e\in I(v)$. A fan is a collection of con…