相关论文: A general Hilbert-Mumford Criterion

Let $X$ be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group $G$. In this paper we provide sufficient conditions, formulated in terms of weight combinatorics, for the…

Let G be a torus of dimension n > 1 and M a compact Hamiltonian G-manifold with $M^G$ finite. A circle, $S^1$, in G is generic if $M^G = M^{S^1}$. For such a circle the moment map associated with its action on M is a perfect Morse function.…

We formulate a conjecture on actions of the multiplicative group in motivic homotopy theory. In short, if the multiplicative group G_m acts on a quasi-projective scheme U such that U is attracted as t approaches 0 in G_m to a closed subset…

Let X be a normal affine algebraic variety with regular action of a torus \TT and T\subset\TT be a subtorus. We prove that each root of X with respect to T can be obtained by restriction of some root of X with respect to \TT. This allows to…

Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial,…

Let $Y$ be a complete intersection in an affine variety $X$, with action by a complex reductive group $G$. Let $T \subset G$ be a maximal torus. A character $\theta$ of $G$ defines GIT quotients $Y//_\theta G$ and $X//_\theta T$. We prove…

Let $H$ be a diagonalizable group over an algebraically closed field $k$ of positive characteristic, and $X$ a normal $k$-variety with an $H$-action. Under a mild hypothesis, e.g. $H$ a torus or $X$ quasiprojective, we construct a certain…

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,…

We give an algebraic proof of a result, due to Bialynicki-Birula and Sommese, characterizing the invariant open subsets of a normal proper variety equipped with a $\mathbf{G}_m$-action that admit a proper good quotient. A major ingredient…

We propose a method to compute a desingularization of a normal affine variety X endowed with a torus action in terms of a combinatorial description of such a variety due to Altmann and Hausen. This desingularization allows us to study the…

We give a valuative criterion for when a smooth algebraic stack with a separated good moduli space is the quotient of a separated Deligne-Mumford stack by a torus. For doing so, we introduce a new class of morphisms, the so-called effective…

A Hamiltonian action of a complex torus on a symplectic complex manifold is said to be {\it multiplicity free} if a general orbit is a lagrangian submanifold. To any multiplicity free Hamiltonian action of a complex torus $T\cong…

Let $X$ be a $\mathbb{Q}$-factorial compact K\"ahler klt threefold admitting an action of a free abelian group $G$, which is of positive entropy and of maximal rank. After running the $G$-equivariant log minimal model program, we show that…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

Let $ \Omega \subset \mathbb{C}^m $ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. Suppose that $\mathcal{M}_q$ is the quotient Hilbert module obtained from a…

The object of this paper is to prove some general results about rational idempotents for a finite group $G$ and deduce from them geometric information about the components that appear in the decomposition of the Jacobian variety of a curve…

Let X be a Hausdorff topological group and G a locally compact subgroup of X. We show that the natural action of G on X is proper in the sense of R. Palais. This is applied to prove that there exists a closed set F of X such that FG=X and…

We consider actions of complex algebraic groups $\mathbf{G}$ on complex algebraic varieties $\mathbf{X}$, coming from actions of real forms $G$ of $\mathbf{G}$ and $X$ of $\mathbf{X}$. We explore the links between the real points of the…

For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant…

In this paper, we investigate quantum Fourier analysis on subfactors and unitary fusion categories. We prove the complete positivity of the comultiplication for subfactors and derive a primary $n$-criterion of unitary categorifcation of…