Incidence relations among the Schubert cells of equivariant punctual Hilbert schemes

摘要

Let ${mathbb H}_{ab}(H)$ be the equivariant Hilbert scheme parametrizing the zero dimensional subschemes of the affine plane $k^2$ , fixed under the one dimensional torus $T_{ab}={(t^{-b},t^a), tin k^*}$ and whose Hilbert function is H. This Hilbert scheme admits a natural stratification in Schubert cells which extends the notion of Schubert cells on Grassmannians. However, the incidence relations between the cells become more complicated than in the case of Grassmannians. In this paper, we give a necessary condition for the closure of a cell to meet another cell. In the particular case of Grassmannians, it coincides with the well known necessary and sufficient incidence condition. There is no known example showing that the condition wouldn't be sufficient.