相关论文: On Zariski's pairs of m-th canonical discriminant …

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…

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…

In this article, examples of Zariski pairs $(B_1, B_2)$ satisfying the following condition are given: (i) $\deg B_1 = \deg B_2 = 7$. (ii) Irreducible components of $B_i$ $(i = 1, 2)$ are lines and conics. (iii) Singularities of $B_i$ $(i =…

We prove that there is an infinite sequence of pairs of plane cuspidal curves $C_{m,1}$ and $C_{m,2}$, such that the pairs $(\Bbb CP^2, C_{m,1})$ and $(\Bbb CP^2, C_{m,2})$ are diffeomorphic, but $C_{m,1}$ and $C_{m,2}$ have non-equivalent…

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 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 manuscript we prove that if two cuspidal plane curves have equivalent braid monodromy factorizations, then they are smoothly isotopic in the plane. As a consequence of this and the Chisini conjecture, we obtain that if two…

Chisini's conjecture asserts that for a cuspidal curve $B\subset \mathbb P^2$ a generic morphism $f$ of a smooth projective surface onto $\mathbb P^2$ of degree $\geq 5$, branched along $B$, is unique up to isomorphism. We prove that if…

This paper is devoted to a very classical problem that can be summarized as follows: let S be a non singular compact complex surface, f:S --> P^2 a finite morphism having simple branching, B the branch curve: to what extent does B determine…

We study complex plane projective sextic curves with simple singularities up to equisingular deformations. It is shown that two such curves are deformation equivalent if and only if the corresponding pairs are diffeomorphic. A way to…

A series of Zariski pairs and four Zariski triplets were found by using lattice theory of K3 surfaces. There is a Zariski triplet of which one member is a deformation of another.

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 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…

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 consider a large class of matrix problems, which includes the problem of classifying arbitrary systems of linear mappings. For every matrix problem from this class, we construct Belitskii's algorithm for reducing a matrix to a canonical…

We prove that the moduli space of double covers ramified at two points $\mathcal{R}_{g,2}$ is uniruled for $3\leq g\leq 6$ and of general type for $g\geq 16$. Furthermore, we consider Prym-canonical divisorial strata in the moduli space…

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

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 show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical…

We prove the existence of three irreducible curves $C_{12,m}$ of degree 12 with the same number of cusps and different Alexander polynomials. This exhibits a Zariski triple. Moreover we provide a set of generators for the elliptic threefold…