Related papers: On the Inheritance of Orbifold Substructures

Cofibration categories are a formalization of homotopy theory useful for dealing with homotopy colimits that exist on the level of models as colimits of cofibrant diagrams. In this paper, we deal with their enriched version. Our main result…

We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of…

The purpose of this article is to study the deformations of smooth surfaces $X$ of general type whose canonical map is a finite, degree 2 morphism onto a minimal rational surface or onto $\mathbf F_1$, embedded in projective space by a very…

A binary three-dimensional (3D) image $I$ is well-composed if the boundary surface of its continuous analog is a 2D manifold. Since 3D images are not often well-composed, there are several voxel-based methods ("repairing" algorithms) for…

We study the problem of folding a polyomino $P$ into a polycube $Q$, allowing faces of $Q$ to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of $P$ or can…

In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. If they are bi-double then they are all fiber…

In [BFMT17] we introduced orbital degeneracy loci as generalizations of degeneracy loci of morphisms between vector bundles. Orbital degeneracy loci can be constructed from any stable subvariety of a representation of an algebraic group. In…

In two-dimensional conformal field theory, we analyze conformally invariant boundary conditions which break part of the bulk symmetries. When the subalgebra that is preserved by the boundary conditions is the fixed algebra under the action…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

''Positive geometries'' are a class of semi-algebraic domains which admit a unique ''canonical form'': a logarithmic form whose residues match the boundary structure of the domain. The study of such geometries is motivated by recent…

We compare algebraic and analytic pictures relevant to the study of birational invariants. Motivated by recent advances in the development of non-commutative Hodge structures, we examine their implication for quiver gauge field theory on…

We construct pairs and continuous families of isospectral yet locally non-isometric orbifolds via an equivariant version of Sunada's method. We also observe that if a good orbifold $\mathcal{O}$ and a smooth manifold $M$ are isospectral,…

We ask about the simply connected compact smooth 6-manifolds which can support structures of Calabi-Yau threefolds. In particular, we study the interesting case of Calabi-Yau threefolds $X$ with second betti number 3. We have a cup-product…

Every cusped, finite-volume hyperbolic three-manifold has a canonical decomposition into ideal polyhedra. We study the canonical decomposition of the hyperbolic manifold obtained by filling some (but not all) of the cusps with solid tori:…

We review coupled ${\rm SU}(3)$-structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry. In particular, we study special classes of examples admitting such structures and the behaviour of…

We classify the 3-dimensional hyperbolic polyhedral orbifolds that contain no embedded essential 2-suborbifolds, up to decomposition along embedded hyperbolic triangle orbifolds (turnovers). We give a necessary condition for a 3-dimensional…

We prove that, for any two polyhedral manifolds $\mathcal P,\mathcal Q$, there is a polyhedral manifold $\mathcal I$ such that $\mathcal P,\mathcal I$ share a common unfolding and $\mathcal I,\mathcal Q$ share a common unfolding. In other…

In the present paper, we investigate whether an embedding of a decomposition space $\mathcal{D}\left(\mathcal{Q},L^{p},Y\right)$ into a given Sobolev space $W^{k,q}(\mathbb{R}^{d})$ exists. As special cases, this includes embeddings into…

Let X be a complex projective n-dimensional manifold of general type, whose canonical system is composite with a pencil. If the Albanese map is generically finite, but not surjective, or if the irregularity is strictly larger than n and the…

We introduce two polynomials (in $q$) associated with a finite poset $P$ that encode some information on the covering relation in $P$. If $P$ is a distributive lattice, and hence $P$ is isomorphic to the poset of dual order ideals in a…