$NS(X)$. It is a free ${\mathbf{Z}}$-module, whose rank is denoted by $\rho(X)$, and called the Picard number of $X$. The real Néron-Severi space ${NS(X)_{{\mathbf{R}}}}$ is just the real subspace of dimension $\rho(X)$ in ${H^{1,1}_{{\partial\overline{\partial}}}(X,{\mathbf{R}})}$ generated by $NS(X)$. Kodaira’s embedding theorem can be formulated as follows: $X$ is a projective manifold iff the intersection of the Kähler cone ${\mathcal{K}}$ with ${NS(X)_{{\mathbf{R}}}}$ is non-empty. Similarly, $X$ is a Moishezon manifold (i.e. bimeromorphic to a projective manifold) iff the intersection of the big cone ${\mathcal{B}}$ with ${NS(X)_{{\mathbf{R}}}}$ is non-empty (cf. \[DP01\]).

Currents with analytic singularities
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### Definition

A closed almost positive $(1,1)$-current $T$ on a compact complex $n$-fold $X$ is said to have analytic singularities (along a subscheme $V({\mathcal{I}})$ defined by a coherent ideal sheaf ${\mathcal{I}}$) if there exists some $c>0$ such that $T$ is locally congruent to $\frac{c}{2}dd^c\log(|f_1|^2+...+|f_k|^2)$ modulo smooth forms, where $f_1,...,f_k$ are local generators of ${\mathcal{I}}$. $T$ is thus smooth outside the support of $V({\mathcal{I}})$, and it is an immediate consequence of the Lelong-Poincaré formula that $\sum\nu(T,D)D$ is just $c$ times the divisor part of the scheme $V({\mathcal{I}})$. If we first blow-up $X$ along $V({\mathcal{I}})$ and then resolve the singularities, we get a modification $\mu:{\widetilde}{X}\to X$, where ${\widetilde}{X}$ is 