3 citations · 5 across the 3 of their papers we have counts for
8 papers
Fiber fans and toric quotients
Alastair Craw, Diane Maclagan
The GIT chamber decomposition arising from a subtorus action on a quasiprojective toric variety is a polyhedral complex. Denote by Sigma the fan that is the cone over the polyhedra…
Uniform bounds on multigraded regularity
Diane Maclagan, Gregory G. Smith
We give an effective uniform bound on the multigraded regularity of a subscheme of a smooth projective toric variety X with a given multigraded Hilbert polynomial. To establish thi…
The toric Hilbert scheme of a rank two lattice is smooth and irreducible
Diane Maclagan, Rekha R. Thomas
The toric Hilbert scheme of a lattice L in Z^n is the multigraded Hilbert scheme parameterizing all ideals in k[x_1,...,x_n] with Hilbert function value one for every degree in the…
Supernormal Vector Configurations
Serkan Hosten, Diane Maclagan, Bernd Sturmfels
A configuration of lattice vectors is supernormal if it contains a Hilbert basis for every cone spanned by a subset. We study such configurations from various perspectives, includi…
The vertex ideal of a lattice
Serkan Hosten, Diane Maclagan
We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the p…
Combinatorics of the toric Hilbert scheme
Diane Maclagan, Rekha R. Thomas
The toric Hilbert scheme is a parameter space for all ideals with the same multi-graded Hilbert function as a given toric ideal. Unlike the classical Hilbert scheme, it is unknown…