相关论文: Existence of Dicritical Divisors Revisited

In this work we deal with dicritical divisors, curvettes and polynomials. These objects have been one of the main research interests of S.S. Abhyankar during his last years. In this work we provide some elementary proofs of some S.S.…

We study dicritical divisors and Rees valuations.

In geometric terms, given a singular foliation of the plane, a dicritical divisor is (whenever it exists) an irreducible component of the exceptional divisor which is transverse to the foliation. Abhyankar gave recently a definition of the…

In [AL11], S.S Abhyankar and I. Luengo introduce a new theory of dicritical divisors in the most general framework. Here we simplify and generalize their results (see Theorems 3.1 and 3.2).

Higher diameters of Cayley digraphs are defined and studied.

The aim of this paper is to provide another perspective on secant varieties on algebraic curves by reformulating the problem in terms of refined de Jonqui\`eres divisors, that is divisors on the curve with prescribed multiplicities and…

We discuss the work of Abhyankar on dicritical divisors with a special focus on the algebraic aspects of this work. We also discuss related work on local quadratic transforms, infinitely near points and Rees valuation rings of an ideal.

Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.

Notion of an open system of second order is introduced. Characteristic function for such an open system is obtained. Model representations of a quadratic non-self-adjoint operator pencil are found.

In this paper we establish the existence of the extended Dirichlet space for nonlinear Dirichlet forms under mild conditions. We employ it to introduce and characterize criticality (recurrence) and subcriticality (transience) and establish…

The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…

We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…

Non-self-adjoint second-order differential pencils on a finite interval with non-separated quasi-periodic boundary conditions and jump conditions are studied. We establish properties of spectral characteristics and investigate the inverse…

A review of a new separability theory based on degenerated Poisson pencils and the so-called separation curves is presented. This theory can be considered as an alternative to the Sklyanin theory based on Lax representations and the…

This paper develops the theory of distinguished regular supercuspidal representations, and it highlights how the correspondence between regular characters and regular supercuspidal representations resembles induction in certain ways.

In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…

We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Then…