Explicit decomposition theorem for special Schubert varieties

Abstract

Abstract We provide an explicit canonical description of the perverse cohomology sheaves and of the primitive perverse cohomology complexes for the non-small resolution π : 𝒮 ~ → 𝒮 {\pi:\tilde{\mathcal{S}}\to\mathcal{S}} of a special Schubert variety 𝒮 {\mathcal{S}} . For such a resolution, we also discuss a way to obtain an explicit splitting of R ⁢ π ⁢ ℚ 𝒮 ~ * {R\pi{{}_{*}}\mathbb{Q}_{\widetilde{{\mathcal{S}}}}} , in the derived category, by means of Gysin morphisms and cohomology extensions.