相关论文: The Analytic Classification of Plane Branches

Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…

Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.

We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.

In this paper, we establish the Zariski decompositions of arithmetic R-divisors of continuous type on arithmetic surfaces and investigate several properties. We also develop the general theory of arithmetic R-divisors on arithmetic…

We study the S-integral points on the complement of a union of hyperplanes in projective space, where S is a finite set of places of a number field k. In the classical case where S consists of the set of archimedean places of k, we…

In this paper we study the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relation between the topology and certain torsion classes in the Picard group of degree zero of the…

We use tools of mathematical logic to analyse the notion of a path on an complex algebraic variety, and are led to formulate a "rigidity" property of fundamental groups specific to algebraic varieties, as well as to define a bona fide…

In this paper, we continue the study of the embedded topology of plane algebraic curves. We study the realization space of conic line arrangements of degree $7$ with certain fixed combinatorics and determine the number of connected…

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We investigate Zariski multiples of plane curves $Z_1, \dots, Z_N$ such that each $Z_i$ is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the…

In this paper, we give a class of reconstructible graphs.

While many classes of cutting-planes are at the disposal of integer programming solvers, our scientific understanding is far from complete with regards to cutting-plane selection, i.e., the task of selecting a portfolio of cutting-planes to…

We investigate similarity classes of arithmetic lattices in the plane. We introduce a natural height function on the set of such similarity classes, and give asymptotic estimates on the number of all arithmetic similarity classes,…

In a previous paper (q-alg/9501022) we suggested some algorithms that could be useful in solving the problem of knot classification. Here we continue this discussion by answering questions raised in that paper and by commenting on practical…

In this paper we prove the following theorem. Let $f:\mathbb{A}^2\rightarrow \mathbb{A}^2$ be a dominate polynomial endomorphisms defined over an algebraically closed field $k$ of characteristic $0$. If there are no nonconstant rational…

We provide a classification result on nearly free arrangements of lines in the complex projective plane with nodes and triple points.

The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…

We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is…

In this article we give a panoramic view on semi-classical analysis.

We construct spectral decomposition of 1D Fokker - Planck differential operator. This reveal solution of Cauchy problem. We develop fundamental solution of Cauchy problem and compare it with one obtained by other means in our former work…