Related papers: Torus actions in the normalization problem

We consider a sheaf of exterior algebras on a simplicial poset $S$ and introduce a notion of homological characteristic function. Two natural objects are associated with these data: a graded sheaf $\mathcal{I}$ and a graded cosheaf…

We describe explicitly the normalization of affine varieties with an algebraic torus action of complexity one in terms of polyhedral divisors. We also provide a description of homogeneous integrally closed ideals of affine T-varieties of…

A fundamental result in toric topology identifies the cohomology ring of the moment-angle complex $\mathcal{Z}_K$ associated to a simplicial complex $K$ with the Koszul homology of the Stanley--Reisner ring of $K$. By studying cohomology…

We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin by studying GKM-orbifolds, which are more general, before…

We investigate the saturation regime of the condensing symmetric inclusion process on the discrete one-dimensional torus in the thermodynamical limit. In this regime, the total mass concentrates on a finite number of sites, forming…

We study the closure of a complex subtorus in a toric manifold. If the closure of the complex subtorus is a smooth complex submanifold in the toric manifold, then the subtorus action on such submanifold is Hamiltonian. In this case, we may…

The fixed points of a natural torus action on the Hilbert schemes of points in C^2 are quiver varieties of infinite type A. The equivariant cohomology of the Hilbert schemes and quiver varieties can be given the structure of bosonic and…

Let $\mathcal{F}\subset\mathcal{M}(D)$ and let $a, b$ and $c$ be three distinct complex numbers. If, there exist a holomorphic function $h$ on $D$ and a positive constant $\rho$ such that for each $f\in\mathcal{F},$ $f$ and $f^{'}$…

In this short note, we study the bordism problem for group actions on the torus and give examples of groups acting on the torus by diffeomorphisms isotopic to the identity that cannot be extended to an action on a bounding 3-manifold. This…

In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half,…

This paper investigates the relations between modular graph forms, which are generalizations of the modular graph functions that were introduced in earlier papers motivated by the structure of the low energy expansion of genus-one Type II…

We study a gravitational action which is a linear combination of the Hilbert-Palatini term and a term quadratic in torsion and possessing local Poincare invariance. Although this action yields the same equations of motion as General…

In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of…

Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…

This thesis is devoted to the study of geometric properties of affine algebraic varieties endowed with an action of an algebraic torus. It comes from three preprints which correspond to the indicated points (1), (2), (3). Let $X$ be an…

After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing…

Matrix quantum mechanics offers an attractive environment for discussing gravitational holography, in which both sides of the holographic duality are well-defined. Similarly to higher-dimensional implementations of holography, collapsing…

The connection problem for isomonodromic tau functions on the one-punctured torus concerns the ratio between the tau function and its modular transform, associated to dual pants decompositions of the torus. In this paper, we study the…

We establish Ecalle's mould calculus in an abstract Lie-theoretic setting and use it to solve a normalization problem, which covers several formal normal form problems in the theory of dynamical systems. The mould formalism allows us to…

We study holomorphic germs $f:(\mathbb{C}^2, 0) \rightarrow (\mathbb{C}^2,0) with non-invertible differential $df_0$. In order to do this, we search for a modification $\pi:X \rightarrow (\mathbb{C}^2,0)$ (i.e., a composition of point…