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Topological Properties of Cyclic Coverings Branched Along An Ample Divisor

Published online by Cambridge University Press:  20 November 2018

Antonio Lanteri  and
Daniele C. Struppa
Antonio Lanteri
Affiliation:
Universita di Milano, Milano, Italy
Daniele C. Struppa
Affiliation:
Universita di Milano, Milano, Italy
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Let X’ → X be a finite morphism between two complex connected projective k-folds. Since Π is surjective, the Betti numbers of X and X’ are related as follows

(0.1) bi(X) ≦ bi(X’).

In particular, if Π is a cyclic covering and the branch locus A is an ample divisor, (0.1) is in fact an equality for i ≦ k — 1 (see 1.10 or, more generally, [5] ). It seems natural to look for such coverings satisfying

(0.2) bk(X)= bk(X’).

Let us see what happens for k = 2. In this case (0.2) can be rephrased as

(0.3) 2x(Ox) + h1,1 (X) + g(Δ) = 2,

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 3 , 01 June 1989 , pp. 462 - 479
Copyright
Copyright © Canadian Mathematical Society 1989

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