holomorphic convexity
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2014 ◽  
Vol 151 (2) ◽  
pp. 351-376 ◽  
Author(s):  
Fréderic Campana ◽  
Benoît Claudon ◽  
Philippe Eyssidieux

AbstractWe extend to compact Kähler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.


2012 ◽  
Vol 23 (08) ◽  
pp. 1250080 ◽  
Author(s):  
R. V. GURJAR ◽  
SAGAR KOLTE

We will prove that given a genus-2 fibration f : X → C on a smooth projective surface X such that b1(X) = b1(C) + 2, the fundamental group of X is almost isomorphic to π1(C) × π1(E), where E is an elliptic curve. We will also verify the Shafarevich Conjecture on holomorphic convexity of the universal cover of surfaces X with genus-2 fibration X → C such that b1(X) > b1(C).


2010 ◽  
Vol 351 (3) ◽  
pp. 571-585 ◽  
Author(s):  
Per Erik Manne ◽  
Erlend Fornæss Wold ◽  
Nils Øvrelid

2007 ◽  
Vol 59 (1) ◽  
pp. 3-35
Author(s):  
Harald Biller

AbstractWe study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixedn-tuple of elements are dense. In particular, we characterize the compact subsets of ℂnwhich appear as joint spectra of suchn-tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.


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