Parameter spaces of Schubert varieties in hyperplane sections of Grassmannians (Q425283)

In order to describe the geometry of linear sections of the Plücker embedding of Grassmannians it is of interest to know the spaces of Schubert varieties contained in them. In particular, for any partition \(\lambda\) and any hyperplane \(H\) one can construct \(X(\lambda,H)\) the space of Schubert varieties with class \(\sigma_\lambda\) contained in \(G(k,n) \cap H\) and moreover a natural incidence correspondence \(I(\lambda)\) parameterizing pairs of a Schubert variety and a hyperplane containing it.NEWLINENEWLINEThe main object of study of the paper under review is the image of this incidence variety by the second projection \(\pi_2\). In particular, in Theorem 1.2, it is described for Grassmannians of lines, i.e. \(k=2\). In Theorem 1.3, also for Grassmannians of lines, \(X(\lambda, H)\) is described in cases where it is non empty.