Related papers: Coarse and pointwise tangent fields

It is shown that the family of all homogeneous continua in the hyperspace of all subcontinua of any finite-dimensional Euclidean cube or the Hilbert cube is an analytic subspace of the hyperspace which contains a topological copy of the…

Here are two of our main results: Theorem 1. Let X be a normal space with dim X=n and m\geq n+1. Then the space C*(X,R^m) of all bounded maps from X into R^m equipped with the uniform convergence topology contains a dense G_{\delta}-subset…

We give a framework to describe abelian bosonic topological systems with parity symmetry on a torus in terms of the projective representation of $GL(2,\mathbb{Z})$. However, this information alone does not guarantee that we can assign…

Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection…

We describe the indecomposable components of the tangent bundle of the punctual Hilbert scheme of a smooth projective surface. As an application, we prove a recent conjecture about classification of products of punctual Hilbert schemes of…

We consider elliptic surfaces $\mathcal{E}$ over a field $k$ equipped with zero section $O$ and another section $P$ of infinite order. If $k$ has characteristic zero, we show there are only finitely many points where $O$ is tangent to a…

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant…

The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has…

Let C be a locally planar curve. Its versal deformation admits a stratification by the genera of the fibres. The strata are singular; we show that their multiplicities at the central point are determined by the Euler numbers of the Hilbert…

Many results about the geometry of the trianguline variety have been obtained by Breuil-Hellmann-Schraen. Among them, using geometric methods, they have computed a formula for the dimension of the tangent space of the trianguline variety at…

The paper concerns the theory of parabolic equations on a broad class of closed subsets of Euclidean space possessing a kind of tangent structure. A necessary framework for considering evolutionary problems is developed, and fundamental…

A class of two-dimensional field theories with exponential interactions is introduced. The interaction depends on two ``coupling'' matrices and is sufficiently general to include all Toda field theories existing in the literature. Lie point…

This paper investigates tangent measures in the sense of Preiss for self-similar sets on ${{\mathbb{R}}^d}$ that satisfy the strong separation condition. Through the dynamics of ``zooming in'' on any typical point, we derive an explicit and…

We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by…

We introduce a theory of relative tangency for projective algebraic varieties. The dual variety $X_Z^\vee$ of a variety $X$ relative to a subvariety $Z$ is the set of hyperplanes tangent to $X$ at a point of $Z$. We also introduce the…

Starting with a minimal model for the CuO$_2$ planes with the on-site Hilbert space reduced to only three effective valence centers [CuO$_4$]$^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) with different conventional spin and different orbital…

We calculate the area, edge and corner Renyi entanglement entropies in the ground state of the transverse-field Ising model, on a simple-cubic lattice, by high-field and low-field series expansions. We find that while the area term is…

We prove a Cayley-Bacharach-type theorem for points in projective space $\mathbb{P}^n$ that lie on a complete intersection of $n$ hypersurfaces. This is made possible by new bounds on the growth of the Hilbert function of almost complete…

We give examples over arbitrary fields of rings of invariants that are not finitely generated. The group involved can be as small as three copies of the additive group, as in Mukai's examples over the complex numbers. The failure of finite…

It has been known for almost 200 years that some angles cannot be trisected by straightedge and compass alone. This paper studies the set of such angles as well as its complement $\mathcal{T}$, both regarded as subsets of the unit circle…