相关论文: Hilbert schemes of finite abelian group orbits and…

We generalise the notion of Gr\"obner fan to ideals in R[[t]][x_1,...,x_n] for certain classes of coefficient rings R and give a constructive proof that the Gr\"obner fan is a rational polyhedral fan. For this we introduce the notion of…

We give a notion of "combinatorial proximity" among strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees "geometric proximity" of the corresponding points in the Hilbert…

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…

We present two algorithms determining all the complete and simplicial fans admitting a fixed non-degenerate set of vectors $V$ as generators of their 1-skeleton. The interplay of the two algorithms allows us to discerning if the associated…

Let \X be an affine toric variety under a torus \T and let T be a subtorus. The general T-orbit closures in \X and their flat limits are parametrized by the main component H_0 of the toric Hilbert scheme. Further, the quotient torus \T/T…

Following Craw, Maclagan, Thomas and Nakamura's work on Hilbert schemes for abelian groups, we give an explicit description of the G-Hilbert scheme for G equal to a cyclic group of order r, acting on C^3 with weights 1,a,r-a. We describe…

The goal of this paper is to show that the local Gr\"obner fan is a polyhedral fan for ideals in the ring of power series and the homogenized ring of analytic differential operators. We will also discuss about relations between the local…

For $G$ a finite group acting linearly on $\mathbb{A}^2$, the equivariant Hilbert scheme $\operatorname{Hilb}^r[\mathbb{A}^2/G]$ is a natural resolution of singularities of $\operatorname{Sym}^r(\mathbb{A}^2/G)$. In this paper we study the…

We provide a algebro-geometric combinatorial description of geometrically integral geometrically normal varieties endowed with an effective action of an algebraic torus over arbitrary fields. This description is achieved in terms of…

The Groebner fan of an ideal $I\subset k[x_1,...,x_n]$, defined by Mora and Robbiano, is a complex of polyhedral cones in $R^n$. The maximal cones of the fan are in bijection with the distinct monomial initial ideals of $I$ as the term…

We consider the notions of Groebner fan and Newton non-degeneracy for an ideal on a toric variety, extending the two existing notions for ideals on affine spaces. We prove, without assumptions on the characteristic of the base fields, that…

In this article, we first give some elementary proprieties of monoids and fans, then construct a toric scheme over an arbitrary ring, from a given fan. Using Valuative Criterion, we prove that this scheme is separated and give the…

The main goal of this paper is to give explicit descriptions of two maximal cones in the Gr\"obner fan of the Pl\"ucker ideal. These cones correspond to the monomial ideals given by semistandard and PBW-semistandard Young tableaux. For the…

Let $G$ be a reductive group over an algebraically closed field of positive characteristic $p$, good for the root system of $G$. The closures of $G$-orbits in the Hilbert nullcone of the coadjoint representation are conical affine Poisson…

In [19], the authors give minimal embedded toric resolutions of ADE-singularities in C^3 by constructing regular refinements of their dual Newton polyhedrons with the elements of their embedded valuation sets derived from the jet schemes…

In this paper we continue the study of good re-embeddings of affine K-algebras started in [KLR]. The idea is to use special linear projections to find isomorphisms between a given affine K-algebra K[X]/I, where X=(x_1,...,x_n), and…

Let $X(\Delta)$ be the real toric variety associated to a smooth fan $\Delta$. The main purpose of this article is: (i) to determine the fundamental group and the universal cover of $X(\Delta)$, (ii) to give necessary and sufficient…

We introduce the multigraded Hilbert scheme, which parametrizes all homogeneous ideals with fixed Hilbert function in a polynomial ring that is graded by any abelian group. Our construction is widely applicable, it provides explicit…

We define several versions of a class of varieties $X_{\mathfrak{g}}$ attached to a complex reductive Lie algebra $\mathfrak{g}$, generalizing the Hilbert scheme of points on the plane. These include trigonometric and elliptic versions…

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…