Tame Coverings and Fundamental Groups of Algebraic Varieties: Part I: Branch Loci with Normal Crossings; Applications: Theorems of Zariski and Picard

1959 ◽  
Vol 81 (1) ◽  
pp. 46 ◽  
Author(s):  
Shreeram Abhyankar
Keyword(s):  
Fundamental Groups ◽  
Algebraic Varieties ◽  
Tame Coverings

scholarly journals On the fundamental groups of normal varieties

2016 ◽  
Vol 18 (04) ◽  
pp. 1550065 ◽  
Author(s):  
Donu Arapura ◽  
Alexandru Dimca ◽  
Richard Hain
Keyword(s):  
Fundamental Groups ◽  
Algebraic Varieties ◽  
Local Systems ◽  
Normal Variety ◽  
Normal Complex ◽  
Normal Varieties ◽  
Rank One

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of rank one local systems on a normal variety are related to the jump loci of a resolution and of a smoothing of this variety.

scholarly journals Fundamental groups of open algebraic varieties

Topology ◽  
1995 ◽  
Vol 34 (3) ◽  
pp. 509-531 ◽  
Author(s):  
Ichiro Shimada
Keyword(s):  
Fundamental Groups ◽  
Algebraic Varieties

A GENERALIZATION OF LEFSCHETZ-ZARISKI THEOREM ON FUNDAMENTAL GROUPS OF ALGEBRAIC VARIETIES

1995 ◽  
Vol 06 (06) ◽  
pp. 921-932 ◽  
Author(s):  
ICHIRO SHIMADA
Keyword(s):  
Fundamental Groups ◽  
Natural Homomorphism ◽  
Algebraic Varieties

Let X and Y be the complements of divisors on non-singular irreducible closed subvarieties [Formula: see text] and [Formula: see text] in ℙn, respectively. Suppose that dim X+ dim Y≥n+2. Then, for a general g∈PGL (n+1), the natural homomorphism π1(g(X)∩Y)→π1(Y) induces a surjection from Ker (π1(g(X)∩Y)→π1(g(X))) onto π1(Y), and there is a surjection to its kernel from the cokernel of π2(X)→π2(ℙn). In particular, if E⊂ℙn is a hypersurface and 2·dim [Formula: see text], then [Formula: see text] is isomorphic to π1(ℙn\E) for a general g∈PGL (n+1).

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