Asian Journal of Mathematics

INTEGRATION OF MEROMORPHIC COHOMOLOGY CLASSES AND APPLICATIONS

DANIEL BARLET and JON MAGNÚSSON

Abstract

The main purpose of this article is to increase the efficiency of the tools introduced in [B.Mg. 98] and [B.Mg. 99], namely integration of meromorphic cohomology classes, and to generalize the results of [B.Mg. 99]. They describe how positivity conditions on the normal bundle of a compact complex submanifold Y of codimension n + 1 in a complex manifold Z can be transformed into positivity conditions for a Cartier divisor in a space parametrizing n-cycles in Z .

As an application of our results we prove that the following problem has a positive answer in many cases :

Let Z be a compact connected complex manifold of dimension n+p. Let Y ⊂ Z a submanifold of Z of dimension p-1 whose normal bundle N Y|Z is (Griffiths) positive. We assume that there exists a covering analytic family (X s ) s∈S of compact n-cycles in Z parametrized by a compact normal complex space S.

Is the algebraic dimension of Z ≥ p ?

Article information

Source
Asian J. Math., Volume 8, Number 1 (2004), 173-214.

Dates
First available in Project Euclid: 21 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1087840915

Mathematical Reviews number (MathSciNet)
MR2128304

Zentralblatt MATH identifier
1086.32018

Citation

BARLET, DANIEL; MAGNÚSSON, JON. INTEGRATION OF MEROMORPHIC COHOMOLOGY CLASSES AND APPLICATIONS. Asian J. Math. 8 (2004), no. 1, 173--214. https://projecteuclid.org/euclid.ajm/1087840915


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