Incidence relations among the Schubert cells of equivariant Hilbert Schemes

Details Incidence relations among the Schubert cells of equivariant Hilbert Schemes Incidence relations among the Schubert cells of equivariant Hilbert Schemes

2000-05-23

arxiv.org/abs/math/0005233v1

Mathematics

Algebraic Geometry

15 pages, 4 figures

Scientific paper

Let HH_{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), t\in 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.

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