Maclagan, Diane and Hering, M.. (2012) The T-graph of a multigraded Hilbert scheme. Experimental Mathematics, Vol.21 (No.3). pp. 280-297. ISSN 1944-950X

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Abstract

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
ISSN:	1944-950X
Date:	2012
Volume:	Vol.21
Number:	No.3
Page Range:	pp. 280-297
Identification Number:	10.1080/10586458.2012.659569
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/49686

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