相关论文: On the Alexander polynomials of conic-line arrange…

We show that the degree of the Alexander polynomial of an irreducible plane algebraic curve with nodes and cusps as the only singularities does not exceed ${5 \over 3}d-2$ where $d$ is the degree of the curve. We also show that the…

In this paper, we revisit the classical problem of determining osculating conics and sextactic points for a given algebraic curve. Our focus is on a particular family of plane cubic curves known as the Hesse pencil. By employing classical…

We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.

We extend results of Cogolludo-Agustin and Libgober relating the Alexander polynomial of a plane curve $C$ with the Mordell--Weil rank of certain isotrivial families of jacobians over $\mathbf{P}^2$ of discriminant $C$. In the second part…

We provide explicit formulas for the Alexander polynomial of pretzel knots and establish several immediate corollaries, including the characterization of pretzel knots with a trivial Alexander polynomial. As an application, we construct a…

In this paper we construct several arrangements of lines and/or conics that are derived from the geometry of the Klein arrangement of $21$ lines in the complex projective plane.

For arborescent links, we present an efficient method of computing their Alexander polynomials. Applying this method, we express the Alexander polynomials of Montesinos links in terms of certain functions associated to rational tangles…

We introduce a notion of tangential Alexander polynomials for plane curves and study the relation with $\theta$^Alexander polynomial. As an application, we use these polynomials to study a non-reduced degeneration $C_t \to D_0+jL$. We show…

It is known, since works of Burde and de Rham, that one can detect the roots of the Alexander polynomial of a knot by the study of the representations of the knot group into the group of the invertible upper triangular $2x2$ matrices. In…

The present work is a user's guide to the results of a previous paper by the second and third authors, where a description of the space of characters of a quasi-projective variety was given in terms of global quotient orbifold pencils.…

Computing polynomial invariants for knots and links using braid representations relies heavily on finding the trace of Hecke algebra elements. There is no easy method known for computing the trace and hence it becomes difficult to compute…

Properties of the Alexander polynomials of Hurwitz curves are investigated. A complete description of the set of the Alexander polynomials of irreducible Hurwitz curves in the terms of their roots is given.

We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links we consider arise from braids on a fixed number of strings. We explore analogies with…

Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There…

We start with a discussion on Alexander invariants, and then prove some general results concerning the divisibility of the Alexander polynomials and the supports of the Alexander modules, via Artin's vanishing theorem for perverse sheaves.…

In this paper, we compute Alexander polynomials of a torus curve C of type (2, 5), C : f(x, y) = f_2(x, y)^5 + f_5(x, y)^2 = 0, under the assumption that the origin O is the unique inner singularity and f2 = 0 is an irreducible conic. We…

Class polynomials attached to affine Hecke algebras were first introduced by X.~He in \cite{He1}. They play an important role in the study of affine Deligne-Lusztig varieties. Motivated by \cite{He2}, we compute the class polynomials…

The higher order degrees are Alexander-type invariants of complements to an affine plane curve. In this paper we characterize the vanishing of such invariants for transversal unions of plane curves $C'$ and $C''$ in terms of the finiteness,…

Let $f:\CN \rightarrow \C $ be a polynomial, which is transversal (or regular) at infinity. Let $\U=\CN\setminus f^{-1}(0)$ be the corresponding affine hypersurface complement. By using the peripheral complex associated to $f$, we give…

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…