相关论文: Trivializations of moment maps

In this paper we show that the transverse image of the momentum map of a Hamiltonian Lie group action admits a natural integral affine stratification with the property that over each stratum the momentum map is an equivariantly locally…

A well-known theorem of W. Fischer and H. Grauert states that analytic fiber spaces with all fibers isomorphic to a fixed compact connected complex manifold are locally trivial. Motivated by this result, we show that if $k$ is an…

We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.

We introduce a notion of scalar curvature of a twisted generalized Kahler manifold in terms of pure spinors formalism. A moment map framework with a modified action of generalized Hamiltonians on an arbitrary compact generalized Kahler…

The moment map $\mu$ is a central concept in the study of Hamiltonian actions of compact Lie groups $K$ on symplectic manifolds. In this short note, we propose a theory of moment maps coupled with an $\mathrm{Ad}_K$-invariant convex…

A finite dimensional real vector space carrying an action of a real reductive group possesses a moment map and a stratification as defined by Kirwan and Ness. In this article we investigate the properties of the moment map, the Kirwan-Ness…

Let G be a complex reductive group and K a maximal compact subgroup. If X is a smooth projective G-variety, with a fixed (not necessarily integral) K-invariant Kaehler form, then the K-action is Hamiltonian. Let M be the zero fiber of the…

A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…

In this paper we prove that a quiver scheme in characteristic zero is reduced if the moment map is flat. We use the reducedness result to show that the equivariant integration formula computes the K-theoretic Nekrasov partition function of…

For a complex reductive group G acting linearly on a complex affine space V with respect to a character, we show two stratifications of V associated to this action (and a choice of invariant inner product on the Lie algebra of the maximal…

We prove that the Marsden-Weinstein reductions for the moment map associated to representations of a quiver are normal varieties. We give an application to conjugacy classes of matrices.

In this paper, we consider generalized moment maps for Hamiltonian actions on $H$-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness…

Let $H$ be a complex linear algebraic group with internally graded unipotent radical acting on a complex projective variety $X$. Given an ample linearisation of the action and an associated Fubini-Study K\"ahler form which is invariant for…

For a quiver without loops with many edges, we generalize the methods of Kac, Crawley-Boevey and Reineke and compute the dimension of Harder-Narasimhan strata of the zero set of the moment map. We notice a link between this dimension and…

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg…

The Reduction Map Theorem in H. Tsuji's work on numerical trivial fibrations is corrected and proven. To this purpose various definitions of Tsuji's new intersection numbers for pseudo-effective line bundles equipped with a positive…

Let V be the vector space of all skew-symmetric (non-associative) complex algebras of dimension n and L the algebraic subset of V of all Lie algebras. We consider the moment map for the action of GL(n) on the projective space P(V) and study…

We introduce the notion of a Nakajima bundle representation. Given a labelled quiver and a variety or manifold $X$, such a representation involves an assignment of a complex vector bundle on $X$ to each node of the doubled quiver; to the…

Let G be a complex semisimple Lie group, K a maximal compact subgroup and V an irreducible representation of K. Denote by M the unique closed orbit of G in P(V) and by O its image via the moment map. For any measure on M we construct a map…

Let C $\rightarrow$ Spec(R) be a relative proper flat curve over an henselian base. Let G be a reductive C-group scheme. Under mild technical assumptions, we show that a G-torsor over C which is trivial on the closed fiber of C is locally…