Search results for "Transformation"
showing 10 items of 1634 documents
$$O_2(\mathbb {C})$$O2(C)-Vector Bundles and Equivariant Real Circle Actions
2020
The main goal of this article is to give an expository overview of some new results on real circle actions on affine four-space and their relation to previous results on \(O_2(\mathbb {C})\)-equivariant vector bundles. In Moser-Jauslin (Infinite families of inequivalent real circle actions on affine four-space, 2019, [13]), we described infinite families of equivariant real circle actions on affine four-space. In the present note, we will describe how these examples were constructed, and some consequences of these results.
q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors
1993
We present the q-deformation of the Lorentz algebra, with Hopf structure, in terms of four independent harmonic oscillators. The explicit realization of the q-Fock space is given and the irreducible finite-dimensional representations of so(1,3)q are described and characterized by its two q-Casimir operators. The concept of irreducible q-Lorentz tensor is also introduced. The analysis is made for a real deformation parameter.
Some overdetermined problems related to the anisotropic capacity
2018
Abstract We characterize the Wulff shape of an anisotropic norm in terms of solutions to overdetermined problems for the Finsler p-capacity of a convex set Ω ⊂ R N , with 1 p N . In particular we show that if the Finsler p-capacitary potential u associated to Ω has two homothetic level sets then Ω is Wulff shape. Moreover, we show that the concavity exponent of u is q = − ( p − 1 ) / ( N − p ) if and only if Ω is Wulff shape.
Cyclic covers of affine T-varieties
2015
Abstract We consider normal affine T -varieties X endowed with an action of finite abelian group G commuting with the action of T . For such varieties we establish the existence of G-equivariant geometrico-combinatorial presentations in the sense of Altmann and Hausen. As an application, we determine explicit presentations of the Koras–Russell threefolds as bi-cyclic covers of A 3 equipped with a hyperbolic G m -action.
On exotic affine 3-spheres
2014
Every A 1 \mathbb {A}^{1} -bundle over A ∗ 2 , \mathbb {A}_{\ast }^{2}, the complex affine plane punctured at the origin, is trivial in the differentiable category, but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of such algebraic bundles are considered; in particular, the complex affine 3 3 -sphere S C 3 , \mathbb {S}_{\mathbb {C}}^{3}, given by z 1 2 + z 2 2 + z 3 2 + z 4 2 = 1 , z_{1}^{2}+z_{2}^{2}+z_{3}^{2}+z_{4}^{2}=1, admits such a structure with an additional homogeneity property. Total spaces of nontrivial homogeneous A 1 \mathbb {A}^{1} -bundles over A ∗ 2 \mathbb {A}_{\ast }^{2} are classified up to G m \mathbb {G}_{m}…
Noncancellation for contractible affine threefolds
2011
We construct two nonisomorphic contractible affine threefolds X X and Y Y with the property that their cylinders X × A 1 X\times \mathbb {A}^{1} and Y × A 1 Y\times \mathbb {A}^{1} are isomorphic, showing that the generalized Cancellation Problem has a negative answer in general for contractible affine threefolds. We also establish that X X and Y Y are actually biholomorphic as complex analytic varieties, providing the first example of a pair of biholomorphic but not isomorphic exotic A 3 \mathbb {A}^{3} ’s.
Uniform estimates for the local restriction of the Fourier transform to curves
2013
We prove sharp estimates, with respect to the ane arclength measure, for the restriction of the Fourier transform to a class of curves in R^d that includes curves of nite type. This measure possesses certain invariance and mitigation properties which are important in establishing uniform results. Peer reviewed
Self-affine sets with fibered tangents
2016
We study tangent sets of strictly self-affine sets in the plane. If a set in this class satisfies the strong separation condition and projects to a line segment for sufficiently many directions, then for each generic point there exists a rotation $\mathcal O$ such that all tangent sets at that point are either of the form $\mathcal O((\mathbb R \times C) \cap B(0,1))$, where $C$ is a closed porous set, or of the form $\mathcal O((\ell \times \{ 0 \}) \cap B(0,1))$, where $\ell$ is an interval.
Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems
2005
In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K is any separately Holder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in \cite{CCS} some applications of Devroye inequality to statistical properties of this class…
𝔸1-contractibility of affine modifications
2019
We introduce Koras–Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine [Formula: see text]-contractible [Formula: see text]-folds. Moreover, we give examples of stably [Formula: see text]-contractible smooth affine [Formula: see text]-folds containing a Brieskorn–Pham surface, and a family of smooth affine [Formula: see text]-folds with a higher-dimensional [Formula: see text]-contractible total space.