Related papers: Zariski pairs on sextics I

We present new families of weighted homogeneous and Newton non-degenerate line singularities that satisfy the Zariski multiplicity conjecture.

We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.

Method of derivation of the duality relations for two-dimensional Z(N)-symmetric spin models on finite square lattice wrapped on the torus is proposed. As example, exact duality relations for the nonhomogeneous Ising model (N=2) and the…

The notion of Zariski pairs for projective curves in $\mathbb P^2$ is known since the pioneer paper of Zariski \cite{Zariski} and for further development, we refer the reference in \cite{Bartolo}.In this paper, we introduce a notion of…

A pair of plane curves with the same combinatorics is said to be (a) a Zariski pair if the plane curves have different embedded topology, and (b) a strong Ziegler pair if their Milnor algebra are not isomorphic. We show that some examples…

We show that the semigroup Zariski topology on a group can be strictly coarser than the group Zariski topology on it, answering a question of Elliott, Jonusas, Mesyan, Mitchell, Morayne, and Peresse.

We show that the fundamental group of the complement of any irreducible tame torus sextics in $\bf P^2$ is isomorphic to $\bf Z_2*\bf Z_3$ except one class. The exceptional class has the configuration of the singularities $\{C_{3,9},3A_2\}$…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

Using the invariant developed in [6], we differentiate four arrangements with the same combinatorial information but in different deformation classes. From these arrangements, we construct four other arrangements such that there is no…

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.…

We prove that termination of lower dimensional flips for generalized klt pairs implies termination of flips for log canonical generalized pairs with a weak Zariski decomposition. Moreover, we prove that the existence of weak Zariski…

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…

Alexander polynomials of sextics with only simple singularities or sextics of torus type with arbitrary singularities are computed. We show that for ieeducible sextics,there are four possibilities: $(t^2-t+1)^j, j=0,1,2,3$.

We characterize the Zariski topologies over an algebraically closed field in terms of general dimension-theoretic properties. Some applications are given to complex manifold and to strongly minimal sets.

We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.

The $n$-th Zariski topology on a group $G$ is generated by the sub-base consiting of the cozero sets of monomials of degree $\le n$ on $G$. We prove that for each group $G$ the 2-nd Zariski topology is not discrete and present an example of…

We study a lattice duality among families of $K3$ surfaces associated to coupling pairs that admit polytope duality with trivial toric contribution.

We show that the existence of a birational weak Zariski decomposition for a pseudo-effective generalized polarized lc pair is equivalent to the existence of a generalized polarized log terminal model.

The purpose of this paper is to exhibit infinite families of conjugate projective curves in a number field whose complement have the same abelian fundamental group, but are non-homeomorphic. In particular, for any $d>3$ we find Zariski…

We give a short proof of the Zariski-Lipman conjecture for toric varieties: any complex toric variety with locally free tangent sheaf is smooth.