Related papers: Relating derived equivalences for simplices of hig…
A matrix $T \in \M_n(\C)$ is \emph{UECSM} if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we…
We study algebro-geometric properties of determinantal loci of (n+1)th symmetric matrices and also their double covers for even ranks. Their singularities, Fano indices and birational geometries are studied in general. The double covers of…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
Given a central extension of Lie groups, we study the classification problem of lifting the structure group together with a given connection. For reductive structure groups we introduce a new connective structure on the lifting gerbe…
We show that every indecomposable conical symplectic hypersurface of dimension four is isomorphic to the known one, namely, the Slodowy slice $X_n$ which is transversal to the nilpotent orbit of Jordan type $[2n-2, 1, 1]$ in the nilpotent…
Singular vectors are those for which the quality of rational approximations provided by Dirichlet's Theorem can be improved by arbitrarily small multiplicative constants. We provide an upper bound on the Hausdorff dimension of singular…
There exist as many index-$k$ sublattices of the hexagonal lattice up to isometry as there exist lattice triangles with normalized volume $k$ up to unimodular equivalence, which can be explained using orbifolds. In dimension 3, it was noted…
We analyse divergent diagrams of \(k\)-fold map-germs on \((\mathbb{C}^n,0)\), for $k, n \geq 2$, associated with reflections, adapting to the complex setting the theory of folds associated with involutions on \((\mathbb{R}^n,0)\). In the…
Higher nilpotent analogues of the $A-\infty$-structure are explicitly defined on arbitrary simplicial complexes, generalizing explicit construction of /hep-th/0704.2609. These structures are associated with the higher nilpotent differential…
Let X be a real algebraic surface. The comparison between the volume of real and complex loci of ample divisors D brings us to define the concordance, which is a number between 0 and 1. This number equals 1 when the Picard number is 1, and…
To a finite dimensional representation of a complex Lie group $G$, an associative algebra of adjoint covariant polynomial maps from the direct sum of $m$ copies of the Lie algebra $\mathfrak{g}$ of $G$ into an algebra of complex matrices is…
We study higher-dimensional interlacing Fibonacci sequences, generated via both Chebyshev type functions and $m$-dimensional recurrence relations. For each integer $m$, there exist both rational and integer versions of these sequences,…
We consider the CSLs of 4-dimensional hypercubic lattices. In particular, we derive the coincidence index $\Sigma$ and calculate the number of different CSLs as well as the number of inequivalent CSLs for a given $\Sigma$. The hypercubic…
We present a universal formula for the dimension of the Cartan powers of the adjoint representation of a complex simple Lie algebra (i.e., a universal formula for the Hilbert functions of homogeneous complex contact manifolds), as well as…
This article provides a complete characterization of the conformal classes of product tori and standard flat tori in complex dimension 1 (real dimension 2). Utilizing basic differential geometry methods, our approach contrasts with…
In this note, we shall prove that two smooth projective varieties of dim 2n connected by a Mukai flop have equivalent bounded derived categories. More precisely, let $\phi : X - - \to X^+$ be a Mukai flop with centers $Y \subset X$ and $Y^+…
For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing…
We use the maximal faces of the $m$-cluster complex of type A to describe the m-cluster tilted algebras of type A as quivers with relations. We then classify connected components of m-cluster tilted algebras of type A up to derived…
We present n-dimensional vortex-ring-like and potential-like solutions with unusual properties related to some elliptical differential equations with compact sources. Solutions have almost 3- or 2-dimensional behaviour in the spaces with…
Denote by ${\mathcal D}$ the open unit disc in the complex plane and $\partial {\mathcal D}$ its boundary. Douglas showed through an identical quantity represented by the Fourier coefficients of the concerned function $u$ that…