image $\operatorname{Im}(d)=d(\Weil(X))$ of the degree morphism in (\[complete deg sequence\]), can be assumed contained in the positive orthant $\R^r_+$ of $\R^r\cong\operatorname{Cl}(X)\otimes\R$, being $r$ the Picard number of $X$*.

Recall that every divisor of $X$ is linearly equivalent to a torus invariant divisor. This means that, in the isomorphism $\operatorname{Cl}(X)\otimes\R\cong\R^r$ the cone $\overline{\operatorname{Eff}}(X)\subseteq\operatorname{Cl}(X)\otimes\R$, which is the closure of the cone generated by classes of effective divisors, is identified with cone $\langle Q\rangle$ generated by the columns of $Q$, that is $$\label{iso-coni}
  \overline{\operatorname{Eff}}(X)\cong\langle Q\rangle$$ Let us now introduce the following:

### Notation {#sssez:notazione}

Let $A$ be a $d\times m$ matrix. For any subset $I\subseteq\{1,\ldots,m\}$ we will denote by $A_I$ the sub-matrix of $A$ obtained by considering the columns indexed by $I$, only, and by $A^I$ the complementary sub-matrix of $A_I$ in $A$, that is, the one obtained by considering only the columns not indexed by $I$.

Coming back to the situation of a complete toric variety $X(\Si)$, of dimension $n$ and Picard number $r$, to every cone $\s\in\Si$ one can associate a subset $I\subseteq\{1,\ldots,m=n+r\}$ such that $$\s=\langle V_I\rangle\subseteq N_\R$$ Define $\I_\Si:=\{I\in\mathfrak{P}(\{1,\ldots,m\})\,|\,\langle V_I\rangle\in\Si\}$, that is, $\Si=\{\langle V_I\rangle\,|\,I\in\I_\Si\}$. Then set $$\operatorname{Mov}(Q):=\bigcap_{i=1}^m \langle Q^{\{i\}}\rangle\quad,\quad \operatorname{Nef}(\I):=\bigcap_{I\in\I} \langle Q^I\rangle\quad \text{(for any}\ \I\subseteq\mathfrak{P}(\{1,\ldots,m\})\,)$$ Recall that the cone $\overline{\operatorname{Mov}}(X)$, 