Search results for " TRANSFORMATION"
showing 10 items of 1043 documents
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.
Dimension of self-affine sets for fixed translation vectors
2018
An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…
Extensions of Groups of Gauge Transformations
1989
In this chapter we shall discuss the structure of the infinite-dimensional Lie groups associated to the affine Kac-Moody algebras. We shall also construct the group of the current algebra of a gauge field theory in 3+1 space-time dimensions and we shall study the implications of the commutation relations for the spin-statistics relation in 3+1 dimensions.
Dorronsoro's theorem in Heisenberg groups
2020
A theorem of Dorronsoro from the 1980s quantifies the fact that real-valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions which are independent of the last variable. As an application, we deduce new proofs for certain vertical vs. horizontal Poincare inequalities for real-valued functions on the Heisenberg group, originally due to Austin-Naor-Tessera and Lafforgue-Naor.