Related papers: The main component of the toric Hilbert scheme

Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/_CT and the toric Hilbert scheme H. We introduce a notion of the main component H_0 of H which parameterizes general T-orbit…

Let X be an irreducible affine T-variety. We consider families of affine stable toric T-varieties over X and give a description of the corresponding moduli space as the quotient stack of an open subscheme in a certain toric Hilbert scheme…

We give explicit equations for the Chow and Hilbert quotients of a projective scheme X by the action of an algebraic torus T in an auxiliary toric variety. As a consequence we provide GIT descriptions of these canonical quotients, and…

We want to understand the geometry of all irreducible components of the toric Hilbert scheme. Until now it is known that the coherent component is (up to normalisation) the toric variety associated to the state polytope of the toric ideal.…

A principal toric bundle $M$ is a complex manifold equipped with a free holomorphic action of a compact complex torus $T$. Such a manifold is fibered over $M/T$, with fiber $T$. We discuss the notion of positivity in fiber bundles and…

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 polyhedral complex. In this paper we show that the toric variety…

The torus T of projective space also acts on the Hilbert scheme of subschemes of projective space. The T-graph of the Hilbert scheme has vertices the fixed points of this action, and edges connecting pairs of fixed points in the closure of…

Let $G$ be a finite abelian subgroup of $PGL(r-1,K)=\mathrm{Aut}(\P^{r-1}_K)$. In this paper, we prove that the normalization of the $G$-orbit Hilbert scheme $\Hilb^G(\P^{r-1})$ is described as a toric variety, which corresponds to the…

For a connected reductive group G and a finite-dimensional G-module V, we study the invariant Hilbert scheme that parameterizes closed G-stable subschemes of V affording a fixed, multiplicity-finite representation of G in their coordinate…

For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G be the group of automorphisms of K[[x,y]] sending the ideal…

In this note we study linear systems on complete toric varieties $X$ with an invariant point, whose orbit under the action of the automorphism group of $X$ contains the dense torus $T$ of $X$. We give a characterization of such varieties in…

Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate…

For an affine $T$-variety $X$ with the action of a torus $T$, this paper provides a combinatorial description of $X$ with respect to the action of a subtorus $T' \subset T$ in terms of a $T/T'$-invariant pp-divisor. We also describe the…

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…

Let H_{ab} be the equivariant Hilbert scheme parametrizing the 0-dimensional subschemes of the affine plane invariant under the natural action of the one-dimensional torus T_{ab}:={(t^{-b},t^a), t\in k^*}. We compute the irreducible…

The closure of a generic torus orbit in the flag variety $G/B$ of type $A_{n-1}$ is known to be a permutohedral variety and well studied. In this paper we introduce the notion of a generic torus orbit in the Schubert variety $X_w$ $(w\in…

We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a…

Consider an algebraic torus of small dimension acting on an open subset of a complex vector space, or more generally on a quasiaffine variety such that a separated orbit space exists. We discuss under which conditions this orbit space is…

Given a reductive group $G$ and a parabolic subgroup $P\subset G$, with maximaltorus $T$, we consider (following Dabrowski's work) the closure $X$ of a generic $T$-orbit in $G/P$, and determine in combinatorial termswhen the toric variety…

We study the partial resolutions of singularities related to Hilbert schemes of points on an affine space. Consider a quotient of a vector space $V$ by an action of a finite group $G$ of linear transforms. Under some additional assumptions,…