Portal de Periódicos da CAPES

The T-Graph of a Multigraded Hilbert Scheme

2012; Taylor & Francis; Volume: 21; Issue: 3 Linguagem: Inglês

10.1080/10586458.2012.659569

1944-950X

Milena Hering, Diane Maclagan,

Commutative Algebra and Its Applications

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 . 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. Keywords: Hilbert schemestorus actionsGröbner bases14C0513F2013P10 ACKNOWLEDGMENTS We thank Bernd Sturmfels for stimulating our interest in the T-graph. This paper was written at several mathematical institutes, and we are grateful to the Institute for Mathematics and its Applications, the Mathematical Sciences Research Institute, the Mathematisches Forschungsinstitut Oberwolfach, and the Mittag-Leffler institute for their hospitality. The first author was partially supported by an Oberwolfach Leibniz Fellowship and NSF grant DMS 1001859. The second author was partially supported by EPSRC grant EP/I008071/1. Dedicated to the memory of Mikael Passare.