Related papers: Zariski-van Kampen theorems for singular varieties…

This paper gives an extension of the classical Zariski-van Kampen theorem describing the fundamental groups of the complements of plane singular curves by generators and relations. It provides a procedure for computation of the first…

In 1933, van Kampen described the fundamental groups of the complements of plane complex projective algebraic curves. Recently, Ch\'eniot-Libgober proved an analogue of this result for higher homotopy groups of the complements of complex…

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…

In [DW05] and [DW07], C. Deninger and A. Werner developed a partial p-adic analogue of the classical Narasimhan-Seshadri correspondence between vector bundles and representations of the fundamental group. We will investigate the various…

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

We give conditions under which the monodromy group of an $A$-hypergeometric system is invariant under modifications of the collection of characters $A$. The key ingredient is a Zariski--Lefschetz type theorem for principal $A$-determinants.

As we known, the {\it Seifert-Van Kampen theorem} handles fundamental groups of those topological spaces $X=U\cup V$ for open subsets $U, V\subset X$ such that $U\cap V$ is arcwise connected. In this paper, this theorem is generalized to…

We formulate and prove a weighted version of Zariski's hyperplane section theorem on the topological fundamental groups of the complements of hypersurfaces in a projective space. As an application, we calculate fundamental groups of the…

The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define the monodromy Lagrangian Floer…

We develop a modification of the Zariski--van Kampen approach for the computation of the fundamental group of a trigonal curve with improper fibers. As an application, we list the deformation families and compute the fundamental groups of…

The Zariski theorem says that for every hypersurface in a complex projective (resp. affine) space of dimension at least 3 and for every generic plane in the projective (resp. affine) space the natural embedding generates an isomorphism of…

We study, for plane complex branches of genus one, the topological type of its generic polar curve, as a function of the semigroup of values and the Zariski invariant of the branch. We improve some results given by Casas-Alvero in 2023,…

We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. We use the Zariski-Van Kampen algorithm and exploit the…

We study Torelli-type theorems in the Zariski topology for varieties of dimension at least 2, over arbitrary fields. In place of the Hodge structure, we use the linear equivalence relation on Weil divisors. Using this setup, we prove a…

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…

We find a new Zariski pair with non-isomorphic fundamental groups that consists of degree $ 8 $ conic-line arrangements. Each arrangement has three conics and two lines. We use the Zariski-van Kampen Theorem and some known Coxeter groups to…

In the 1970s O. Zariski introduced a general theory of equisingularity for algebroid and algebraic hypersurfaces over an algebraically closed field of characteristic zero. His theory builds up on understanding the dimensionality type of…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

We show that varieties of dimension at least 2 over infinite fields are determined as abstract schemes by their Zariski topological spaces together with the rational equivalence relation on the set of effective divisors. This gives a…

In algebraic topology, the fundamental groupoid is a classical homotopy invariant which is defined using continuous maps from the closed interval to a topological space. In this paper, we construct a semi-coarse version of this invariant,…