Related papers: Hypersurface singularities with monomial Jacobian …

This paper studies the equivalence between generalized holomorphic functions (GHF) and complex analytic functions in the framework of Robinson-Colombeau generalized numbers. In every non-Archimedean ring, the use of ordinary series is…

We prove that similarly to the standard case, the equilibrium measure of Julia sets of exceptional Jacobi polynomials tends to the equilibrium measure of the interval of orthogonality in weak-star sense.

We study the topological triviality and the Whitney equisingularity of a family of isolated determinantal singularities. On one hand, we give a L\^e-Ramanujam type theorem for this kind of singularities by using the vanishing Euler…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

Let $k$ be a field of characteristic $p>0$ and $R$ be a subalgebra of $k[X]=k[x_1,...,x_n]$. Let $J(R)$ be the ideal in $k[X]$ defined by $J(R)\Omega_{k[X]/k}^n=k[X]\Omega_{R/k}^n$. It is shown that if it is a principal ideal then $J(R)^q$…

Let $A, B$ be polynomial rings over a field $k$, and $I\subseteq A, J\subseteq B$ proper homogeneous ideals. We analyze the associated primes of powers of $I+J\subseteq A\otimes_k B$ given the data on the summands. The associated primes of…

From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…

We consider the tensor power $V=(C^N)^{\otimes n}$ of the vector representation of $gl_N$ and its weight decomposition $V=\oplus_{\lambda=(\lambda_1,...,\lambda_N)}V[\lambda]$. For $\lambda = (\lambda_1 \geq ... \geq \lambda_N)$, the…

This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

Pursuing ideas of Jeff Smith, we develop a homotopy theory of ideals of monoids in a symmetric monoidal model category. This includes Smith ideals of structured ring spectra and of differential graded algebras. Such Smith ideals are NOT…

We develop a theory of quasisymmetries for finitely ramified fractals, with applications to finitely ramified Julia sets. We prove that certain finitely ramified fractals admit a naturally defined class of "undistorted metrics" that are all…

A representation of a finite group $G$ on a finite dimensional vector space $V$ is called \textbf{unisingular} if every $g\in G$ has 1 as an eigenvalue in its action on $V$. In this paper we show that certain unisingular representations can…

For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any…

We define a generalized Jacobian $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and a generalized Picard group $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ of a graph $\mathit{Gr}$ with respect to a modulus $ \mathfrak{m}=\sum_{i=1}^s m_iw_i$ with $w_i$…

We characterize monomial ideals which are intersections of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.

We find all spectral type differential equations satisfied by the symmetric generalized ultraspherical polynomials which are orthogonal on the interval [-1,1] with respect to the classical symmetric weight function for the Jacobi…

Two properties of projective hypersurfaces related to the module of Jacobian derivations, namely being tame and being plus-one generated, are discussed in this paper. Tame hypersurfaces are related to Bourbaki ideals, and free hypersurfaces…

In recent studies on the G-convergence of Beltrami operators, a number of issues arouse concerning injectivity properties of families of quasiconformal mappings. Bojarski, D'Onofrio, Iwaniec and Sbordone formulated a conjecture based on the…

We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…