Related papers: Polynome de Bernstein-Sato generique local

In this paper an explicit form of generalized Chebyshev Koornwinder's type polynomial of first kind in terms of the Bernstein basis of fixed degree $n$ is provided. Moreover, we investigate generalized Chebyshev Koornwinder's type…

In [16] there was proved that any biharmonic hypersurface with at most three distinct principal curvatures in space forms has constant mean curvature. At the very last step of the proof, the argument relied on the fact that the resultant of…

In this article we study holomorphic deformations of the filtered Gauss-Manin systems associated to a vanishing period integral. For that purpose we introduce a new sub-class of the class of monogenic (a,b)-modules (Brieskorn modules) which…

For an ideal of a regular $\cc$-algebra, its Bernstein-Sato polynomial is the monic polynomial of the lowest degree satisfying an Bernstein-Sato functional equation. We generalize the notion of Bernstein-Sato functional equations to the…

Three questions about the intertwining operators for the generalized principal series on a symmetric R-space are solved : description of the functional kernel, both in the compact and the non-compact picture, domain of convergence,…

We prove the following theorem: Fibered Power Theorem: Let $X\rar B$ be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general…

We define new generalized factorials in several variables over an arbitrary subset $\underline{S} \subseteq R^n,$ where $R$ is a Dedekind domain and $n$ is a positive integer. We then study the properties of the fixed divisor…

We consider a continuous family $(f_s)$, $s\in[0,1]$ of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant (or…

We prove that moduli spaces of semistable parabolic bundles and generalized parabolic sheaves (GPS) with a fixed determinant on a smooth projective curve are globally F-regular type. As an application, we prove vanishing theorems on the…

In this paper, we consider the following $(A, B)$-polynomial $f$ over finite field: $$f(x_0,x_1,\cdots,x_n)=x_0^Ah(x_1,\cdots,x_n)+g(x_1,\cdots,x_n)+P_B(1/x_0),$$ where $h$ is a Deligne polynomial of degree $d$, $g$ is an arbitrary…

The Bernstein approximation problem is to determine whether or not the space of all polynomials is dense in a given weighted $C_0$-space on the real line. A theorem of L. de Branges characterizes non--density by existence of an entire…

We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do…

In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its…

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural…

We define the generalized basic hypergeometric polynomial of degree $N \geq 1$ in terms of the generalized basic hypergeometric function, which depends on (arbitrary, generic, possibly complex) parameters $q \neq 1$, the $r \geq 0$…

Let k be an uncountable algebraically closed field and let Y be a smooth projective k-variety which does not admit a decomposition of the diagonal. We prove that Y is not stably birational to a very general hypersurface of any given degree…

Let $f$ be a real function defined on the interval $[0,1]$ which is constant on $(a,b)\subset [0,1]$, and let $B_nf$ be its associated $n$th Bernstein polynomial. We prove that, for any $x\in (a,b)$, $|B_nf(x)-f(x)|$ converges to $0$ as…

There is a convolution product on 3-variable partial flag functions of a locally finite poset that produces a generalized M\"obius function. Under the product this generalized M\"obius function is a one sided inverse of the zeta function…

We generalize the Bernstein-Sato polynomials of Budur, Mustata and Saito to ideals in normal semigroup rings. In the case of monomial ideals, we also relate the roots of the Bernstein-Sato polynomial to the jumping coefficients of the…

We define a generalization of the Brauer group $\operatorname{H}_\mathrm{B}^{n}(X)$ for an equi-dimensional scheme $X$ and $n>0$. In the case where $X$ is the spectrum of a local ring of a smooth algebra over a discrete valuation ring,…