Related papers: The Analytic Classification of Plane Branches

A simple sextic is a reduced complex projective plane curve of degree 6 with only simple singularities. We introduce a notion of Z-splitting curves for the double covering of the projective plane branching along a simple sextic, and…

We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.

The article demonstrates the procedure how to compute the Zariski closure of an orbit by an algebraic action of finitely generated group on the affine plane. First half of the algorithm is about deciding whether given finitely generated…

A couple of complex projective plane curves are said to make a Zariski pair if they have the same degree and the same type of singularities, but their embeddings in the projective plane are topologically different. In this paper, we present…

We introduce the Schur class of functions, discrete analytic on the integer lattice in the complex plane. As a special case, we derive the explicit form of discrete analytic Blaschke factors and solve the related basic interpolation…

In this paper we give an asymptotic bound of the cardinality of Zariski multiples of particular plane singular curves. These curves have only nodes and cusps as singularities and are obtained as branched curves of ramified covering of the…

We present an approach to detecting Zariski pairs in conic line arrangements. Our method introduces a combinatorial condition that reformulates the tubular neighborhood homeomorphism criterion arising in the definition of Zariski pairs.…

Given a family of complex affine planes, we show that it is trivial over a Zariski open subset of the base. The proof relies upon a relative version of the contraction theorem.

We formulate and prove a generalization of Zariski-van Kampen theorem on the topological fundamental groups of smooth complex algebraic varieties. As an application, we prove a hyperplane section theorem of Lefschetz-Zariski-van Kampen type…

This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.

We study the plane automorphisms given by polynomials with certain degree decompositions.

In this paper we summarise the work discussed in Ref. [1] and [2] (q-alg/9505003), in which we introduced a method helpful in solving the problem of knot classification. We also present results obtained since then.

In this article we give an implementation of the standard algorithm to segment a real algebraic plane curve defined implicitly. Our implementation is efficient and simpler than previous. We use global information to count the number of…

In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.

In this present paper, we study the splitting of nodal plane curves with respect to contact conics. We define the notion of splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of…

We discuss different generalizations of Zariski decomposition, relations between them and connections with finite generation of divisorial algebras.

We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.

We settle a long-standing problem in the theory of Hecke algebras of complex reflection groups by constructing many (graded) integral cellular bases of these algebras. As applications, we explicitly construct the simple modules of Ariki's…

In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical…

The purpose of this paper is two-fold. We first prove a series of results, concerned with the notion of Zariski multiplicity, mainly for non-singular algebraic curves. These results are required in the paper "A Theory of Branches for…