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Linearly independent divisors on complex manifolds

Jelonek Z.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

25-30

Let X be a connected normal complex space and let D be a non-zero Cartier divisor on X with the support [...]. We show that if D is a principal divisor then the group H[sub 1](X \ [absolute value of D],Z) cannot be a torsion group. In particular the group H[sub1](H \ [absolute value of D],Z)] must be infinite. As a corollary we prove that simple Cartier divisors D[sub 1],...,D[sub r] on a complex manifold X are linearly independent in Cl(X), provided the group H[sub1](X \ [...] is a torsion group.