Related papers: Zariski Pairs on sextics II

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…

Two arrangements with the same combinatorial intersection lattice but whose complements have different fundamental groups are called a Zariski pair. This work finds that there are at most nine such pairs amongst all ten line arrangements…

Let us consider an $n$-dimensional complex torus $T^{2n}_{J=T}:=\mathbb{C}^n/2\pi(\mathbb{Z}^n \oplus T\mathbb{Z}^n)$. Here, $T$ is a complex matrix of order $n$ whose imaginary part is positive definite. In particular, when we consider the…

A paper torus is an embedded polyhedral torus that is isometric to a flat torus in the intrinsic sense. We prove that there does not exist a paper torus with $7$ vertices, and that there does exist a paper torus with $8$ vertices. This…

In this paper, complement-equivalent arithmetic Zariski pairs will be exhibited answering in the negative a question by Eyral-Oka on these curves and their groups. A complement-equivalent arithmetic Zariski pair is a pair of complex…

We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let $(X,B)$ be a projective log canonical pair. We will show that $(X,B)$ has a log minimal model if either $K_X+B$ birationally…

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.

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 consider surface links in the 4-space which are presented by the form of simple branched coverings over the standard torus, which we call torus-covering links. In this paper, we study unknotting numbers of torus-covering links. In some…

We present remarkable properties of the groups SL2(Z/NZ) which might be useful in detailed studies of some quotients appearing in Conformal Field Theories.

We describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.

Let $G$ be a finite group of Lie type and $T$ a maximal torus of $G$. In this paper we complete the study of the question of the existence of a complement for the torus $T$ in its algebraic normalizer $N(G,T)$. It is proved that every…

In this paper, we present a complete coarse classification of non-loose Legendrian and transverse torus knots in any contact structure on $S^1\times S^2$.

We give a classification up to equisingular deformation and compute the fundamental groups of maximizing plane sextics with a type $\mathbf{E}_6$ singular point.

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

We construct a moduli space of stable projective pairs with a nontrivial action of a connected reductive group. These stable reductive pairs are higher-dimensional analogs of stable n-pointed curves and generalize to the non-commutative…

We give necessary and sufficient conditions for an orthogonal group defined over a field of characteristic not 2 to contain a maximal torus of a given type.

We provide new examples of curves of genus 6 or 10 attaining the Serre bound. They all belong to the family of sextics introduced in [19] as a a generalization of the Wiman sextics [36] and Edge sextics [9]. Our approach is based on a…

All families of sextic surfaces with the maximal number of isolated triple points are found.

We present a method of Zariski-van Kampen type for the calculation of the transcendental lattice of a complex projective surface. As an application, we calculate the transcendental lattices of complex singular K3 surfaces associated with an…