Related papers: On Constructions of Free Singularities
We review properties of affine special Kaehler structures focusing on singularities of such structures in the simplest case of real dimension two. We describe all possible isolated singularities and compute the monodromy of the flat…
We give a systematic and self-contained account of the construction of geometrically decomposed bases and degrees of freedom in finite element exterior calculus. In particular, we elaborate upon a previously overlooked basis for one of the…
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial…
It is well known that free independence is equivalent to the vanishing of mixed free cumulants. The purpose of this short note is to build free products of $*$-probability spaces using this as the definition of freeness and relying on free…
The fundamental group of the complement of a hyperplane arrangement plays an important role in studying the corresponding arrangements. In particular, for large families of hyperplane arrangements, this fundamental group, being isomorphic…
We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented…
We construct new examples of free curve arrangements in the complex projective plane using point-line operators recently defined by the second author. In particular, we construct a new example of a conic-line arrangement with ordinary…
This paper analyses the parabolic geometries generated by a free 3-distribution in the tangent space of a manifold. It shows the existence of normal Fefferman constructions over CR and Lagrangian contact structures corresponding to holonomy…
Using the $E_\infty-$structure on singular cochains, we construct a homotopy coherent map from the cyclic bar construction of the differential graded algebra of cochains on a space to a model for the cochains on its free loop space. This…
We introduce an embedding of the free magma on a set A into the direct product of the free magma on a singleton set and the free semigroup on A. This embedding is then used to prove several theorems related to algebraic independence of…
This paper brings the construction of free medial quandles as well as free $n$-symmetric medial quandles and free $m$-reductive medial quandles.
Given a partition $\lambda$ of n, consider the subspace $E_\lambda$ of $C^n$ where the first $\lambda_1$ coordinates are equal, the next $\lambda_2$ coordinates are equal, etc. In this paper, we study subspace arrangements $X_\lambda$…
In a recent paper [8], it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus…
We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free…
We define and calculate the weighted multiplicities of non Gorenstein terminal singularities on threefolds and some quotient singularities. We improve freeness conditions on threefolds.
We construct for any algebra over an operad an Hochschild chain complex. In the case of the singular cochain complex of a topological space, considered as a commutative algebra up to homotopy, we show that this complex computes the singular…
The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free multiarrangements are…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…
A hypersurface $X\subset \mathbb P^n$ is said to be free if its associated sheaf $T_X$ of vector fields tangent to $X$ is a free ${\mathcal O}_{\mathbb P^n}$-module. So far few examples of free hypersurfaces are known. In this short note,…
In this paper we focus on various aspects of singular complex plane curves, mostly in the context of their homological properties and the associated combinatorial structures. We formulate some challenging open problems that can point to new…