zariski pair
Recently Published Documents


TOTAL DOCUMENTS

4
(FIVE YEARS 0)

H-INDEX

2
(FIVE YEARS 0)

2017 ◽  
Vol 26 (13) ◽  
pp. 1750089 ◽  
Author(s):  
Benoît Guerville-Ballé ◽  
Taketo Shirane

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.


Author(s):  
Enrique Artal Bartolo ◽  
José Ignacio Cogolludo-Agustín ◽  
Benoît Guerville-Ballé ◽  
Miguel Marco-Buzunáriz

2004 ◽  
Vol 8 (3) ◽  
pp. 473-474
Author(s):  
Guangfeng Jiang ◽  
Jainming Yu
Keyword(s):  

2001 ◽  
Vol 10 (04) ◽  
pp. 547-578 ◽  
Author(s):  
E. ARTAL ◽  
J. CARMONA ◽  
J.I. COGOLLUDO ◽  
HIRO-O TOKUNAGA

In this paper we show a Zariski pair of sextics which is not a degeneration of the original example given by Zariski. This is the first example of this kind known. The two curves of the pair have a trivial Alexander polynomial. The difference in the topology of their complements can only be detected via finer invariants or techniques. In our case the generic braid monodromies, the fundamental groups, the characteristic varieties and the existence of dihedral coverings of ℙ2 ramified along them can be used to distinguish the two sextics. Our intention is not only to use different methods and give a general description of them but also to bring together different perspectives of the same problem.


Sign in / Sign up

Export Citation Format

Share Document