Related papers: Geometric realizations of birational transformatio…

We study actions of linear algebraic groups on central simple algebras using algebro-geometric techniques. Suppose an algebraic group G acts on a central simple algebra A of degree n. We are interested in questions of the following type:…

An induced additive action on a projective variety $X\subseteq\mathbb{P}^n$ is a regular action of the group $\mathbb{G}_a^n$ on $X$ with an open orbit that can be extended to a regular action on $\mathbb{P}^n$. Such actions are known to…

We construct a finite dimensional Kaehler manifold with a holomorphic, symplectic circle action whose symplectic reduced spaces may be identified with the tau-vortex moduli spaces (or tau-stable pairs). The Morse theory of the circle action…

We construct toric manifolds of complex dimension $\geq 4$, whose orbit spaces by the action of the compact torus are not homeomorphic to simple polytopes (as manifolds with corners). These provide the first known examples of toric…

Suppose an algebraic torus acts on a complex algebraic variety $X$. Then a great part of information about global invariants of $X$ are encoded in some data localized around the fixed points. The goal of this note is to present a connection…

We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.

Let X be an algebraic variety with a generically free action of a connected algebraic group G. Given an automorphism u of G, we will denote by X^u the same variety X with the G-action given by twisted by u. V. L. Popov asked if X and X^u…

In this note we provide a new perspective on the topological parts of several action functionals in string and M-theory. We show that rationally these can be viewed as large gauge transformations corresponding to variations of higher…

We present a simple and fast embedded resolution of varieties and principalization of ideals using torus actions on ambient smooth varieties with simple normal crossings (SNC) divisors. The canonical functorial resolution in characteristic…

Extending the usual $\mathbf{C}^{\ast r}$ actions of toric manifolds by allowing asymmetries between the various $\mathbf{C}^{\ast}$ factors, we build a class of non commutative (NC) toric varieties $\mathcal{V}%_{d+1}^{(nc)}$. We construct…

In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…

We link small modifications of projective varieties with a ${\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Bia{\l}ynicki-Birula cells, we produce a system of birational equivariant…

We compute the integral cohomology of certain semi-direct products arising from a linear G-action on the n-torus, where G is a finite group. The main application is the complete calculation of torsion gerbes for certain six dimensional…

We define formal geometric quantisation for proper Hamiltonian actions by possibly noncompact groups on possibly noncompact, prequantised symplectic manifolds, generalising work of Weitsman and Paradan. We study the functorial properties of…

In this article, we describe all the group morphisms from the group of orientation-preserving homeomorphisms of the circle to the group of homeomorphisms of the annulus or of the torus.

Let G be an n-dimensional torus and $\tau$ a Hamiltonian action of G on a compact symplectic manifold, M. If M is pre-quantizable one can associate with $\tau$ a representation of G on a virtual vector space, Q(M), by…

Singular actions on C*-algebras are automorphic group actions on C*-algebras, where the group need not be locally compact, or the action need not be strongly continuous. We study the covariant representation theory of such actions. In the…

The paper surveys some new results and open problems connected with such fundamental combinatorial concepts as polytopes, simplicial complexes, cubical complexes, and subspace arrangements. Particular attention is paid to the case of…

For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver…

We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian…