At the end of the following page : The associated Schubert variety of a flag of subspaces of a vector space. , the author says :
Let $[W]\in X=X_{\underline i}$, by construction: \begin{equation} [W]=[v_1\wedge\dots\wedge v_k]=\left[\sum_{\underline{j}\leq\underline{i}}d_{\underline j}e_{\underline j}\right] \end{equation} in particular: \begin{equation} \forall h\in\{1,\dots,k\},\,\dim\left(W\cap F_{i_h}\right)\geq h \end{equation} and vice versa.
Could someone explain to me why have we this, in details please ?
Thanks in advance for your help.