The T-graph of a multigraded Hilbert scheme
Maclagan, Diane and Hering, M.. (2012) The T-graph of a multigraded Hilbert scheme. Experimental Mathematics, Vol.21 (No.3). pp. 280-297. ISSN 1944-950XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1080/10586458.2012.659569
The T-graph of a multigraded Hilbert scheme records the zero and one-dimensional orbits of the T = (K^*)^n action on the Hilbert scheme induced from the T-action on A^n. It has vertices the T-fixed points, and edges the one-dimensional T-orbits. We give a combinatorial necessary condition for the existence of an edge between two vertices in this graph. For the Hilbert scheme of points in the plane, we give an explicit combinatorial description of the equations defining the scheme parameterizing all one-dimensional torus orbits whose closures contain two given monomial ideals. For this Hilbert scheme we show that the T-graph depends on the ground field, resolving a question of Altmann and Sturmfels.
|Item Type:||Journal Article|
|Divisions:||Faculty of Science > Mathematics|
|Journal or Publication Title:||Experimental Mathematics|
|Publisher:||Taylor & Francis|
|Page Range:||pp. 280-297|
|Access rights to Published version:||Restricted or Subscription Access|
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