PageHeader : Funkcialaj Ekvacioj, 38 (1995) 121-157 Title : Foliations on Complex Spaces AuthorInfo : By AuthorInfo : Akihiro SAEKI AuthorInfo : (University of Tokyo, Japan) section : Contents section : 0 Introduction section : 1 Coherent foliations on complex spaces 1.0. Coherent foliations subsection : 1.1. Morphisms and pull-back of foliations subsection : 1.2. Proper modifications and foliations subsection : 1.3. Closed embeddings and foliations subsection : 1.4. Quotient singularities subsection : 1.5. Foliations of dimension one or codimension one subsection : 1.6. Examples . The complex space X defined by $z^{2}$ ?xy $=0$ section : 2. Coherent modules, their duals and their submodules subsection : 2.0. Preliminaries. subsection : 2.1. The $\mathcal{O}_{\mathrm{X}}$ -submodule $\mathscr{T}_{F}$ subsection : 2.2. The $\mathcal{O}_{\mathrm{X}}$ -submodule $\mathscr{T}_{SF}$ subsection : 2.3. The $\mathcal{O}_{\mathrm{X}}$ -submodule $\mathscr{T}^{a\neg l1}$ subsection : 2.4. The $\mathcal{O}_{\mathrm{X}}$ -submodule $\mathscr{T}_{\mathscr{M}}$ subsection : 2.5. Relations of $\mathscr{T}_{F}$ , $\mathscr{T}_{SF}$ and $\mathscr{T}^{a\perp}$ subsection : 2.6. Relations with $\mathscr{T}_{\mathscr{M}}$ section : Appendices subsection : A.0. Algebraic observations on coherent sheaves on reduced complex spaces. subsection : A.1. Algebraic observations on coherent sheaves on locally irreducible complex spaces subsection : A.2. Coherent sheaves of rank 1 section : References