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Elliptic fibrations and holomorphic bundles. (Italian. English summary) Zbl 0725.14032

It is proved that if \(S\to D\) is an algebraic relatively minimal (compact) elliptic surface having a multiple fibre f and if \(S^*\to D^*\) is obtained from \(S\to D\) via a logarithmic transformation along f then \(S^*\) is non-algebraic provided S has non-negative Kodaira dimension.

MSC:

14J27 Elliptic surfaces, elliptic or Calabi-Yau fibrations
14M20 Rational and unirational varieties
32J10 Algebraic dependence theorems
14E99 Birational geometry
32L05 Holomorphic bundles and generalizations
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