Some results about a smooth hyperplane section of a 3-fold of non negative Kodaira dimension

Abstract

1. Let S be a smooth hyperplane section of a smooth, connected, projective threefold X ~ pN of non negative Kodaira dimension. It was conjectured by A. J. Sommese that in this case x((gs)> 3 and h2'~ 3. In [5] Sommese proved that X((gs)> 2 and h 2, 0 (S) > 2. In this paper, using Miyaoka's result [4], we prove Sommese's conjecture under an additional assumption. We want to express our graditude to A. J. Sommese for helpful discussion we had while visiting the University of L'Aquila. We would like to thank the referee for his suggestions.