Fundamental Group of the Complement of Affine Plane Curves

Topology '90 ◽  
2011 ◽  
Author(s):  
Shulim Kaliman
Keyword(s):  
Fundamental Group ◽  
Affine Plane ◽  
Plane Curves

Affine plane curves with one place at infinity

1999 ◽  
Vol 49 (2) ◽  
pp. 375-404 ◽  
Author(s):  
Masakazu Suzuki
Keyword(s):  
Affine Plane ◽  
Plane Curves

scholarly journals ALBANESE VARIETIES OF CYCLIC COVERS OF THE PROJECTIVE PLANE AND ORBIFOLD PENCILS

2016 ◽  
Vol 227 ◽  
pp. 189-213
Author(s):  
E. ARTAL BARTOLO ◽  
J. I. COGOLLUDO-AGUSTÍN ◽  
A. LIBGOBER
Keyword(s):  
Projective Plane ◽  
Fundamental Group ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Plane Curves ◽  
Abelian Surface ◽  
Singular Curve ◽  
Cyclic Covers ◽  
Genus 2 ◽  
Multiple Fibers

The paper studies a relation between fundamental group of the complement to a plane singular curve and the orbifold pencils containing it. The main tool is the use of Albanese varieties of cyclic covers ramified along such curves. Our results give sufficient conditions for a plane singular curve to belong to an orbifold pencil, that is, a pencil of plane curves with multiple fibers inducing a map onto an orbifold curve whose orbifold fundamental group is nontrivial. We construct an example of a cyclic cover of the projective plane which is an abelian surface isomorphic to the Jacobian of a curve of genus 2 illustrating the extent to which these conditions are necessary.

On the fundamental group of the complement of certain singular plane curves

1987 ◽  
Vol 102 (3) ◽  
pp. 453-457 ◽  
Author(s):  
András Némethi
Keyword(s):  
Projective Space ◽  
Fundamental Group ◽  
Algebraic Curve ◽  
Plane Curves ◽  
Image Position

Let C be a complex algebraic curve in the projective space ℙ2. The purpose of this paper is to calculate the fundamental group G of the complement of C in the case when C = X ∩ H1 ∩ … ∩ Hn−2, whereand Hi are generic hyperplanes (i = 1, … n − 2).

scholarly journals Topology of families of affine plane curves

1999 ◽  
Vol 71 (2) ◽  
pp. 129-139
Author(s):  
Hà Vui ◽  
Pham Son
Keyword(s):  
Affine Plane ◽  
Plane Curves

scholarly journals On the Fundamental Group of self-affine plane Tiles

2006 ◽  
Vol 56 (7) ◽  
pp. 2493-2524 ◽  
Author(s):  
Jun Luo ◽  
Jörg M. Thuswaldner
Keyword(s):  
Fundamental Group ◽  
Affine Plane

scholarly journals Non-homotopicity of the linking set of algebraic plane curves

2017 ◽  
Vol 26 (13) ◽  
pp. 1750089 ◽  
Author(s):  
Benoît Guerville-Ballé ◽  
Taketo Shirane
Keyword(s):  
Fundamental Group ◽  
Plane Curves ◽  
Zariski Pair

The linking set is an invariant of algebraic plane curves introduced by Meilhan and the first author. It has been successfully used to detect several examples of Zariski pairs, i.e. curves with the same combinatorics and different embedding in [Formula: see text]. Differentiating Shimada's [Formula: see text]-equivalent Zariski pair by the linking set, we prove, in the present paper, that this invariant is not determined by the fundamental group of the curve.

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