By Klaus Hulek, Thomas Peternell, Michael Schneider, Frank-Olaf Schreyer

The Bayreuth assembly on "Complex Algebraic types" focussed at the class of algebraic kinds and subject matters comparable to vector bundles, Hodge concept and hermitian differential geometry. lots of the articles in this quantity are heavily relating to talks given on the convention: all are unique, totally refereed examine articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: effects on forms with many strains and their functions to adjunction theory.- G. Bohnhorst, H. Spindler: the soundness of convinced vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear structures and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on optimistic line bundles.- T. Fujita: On adjoint bundles of abundant vector bundles.- Y. Kawamata: reasonable degenerations of algebraic surfaces.- U. Persson: Genus fibrations revisited.- Th. Peternell, M. Szurek, J.A. Wisniewski: Numerically potent vector bundles with small Chern classes.- C.A.M. Peters: at the rank of non-rigid interval maps within the weight one and case.- A.N. Tyurin: The geometry of the precise parts of moduli area of vector bundles over algebraic surfaces of common sort.

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**Example text**

2)). Take a line £ in a smooth general fiber pd of p. 2)). Now compute v = - K x ' Z - 2 = - Kpd-Z - 2 = d - 1. 5) applies to give the result. 3) Y is a point, X is therefore a projective space, and the result is clear. 2), p is a composition of a p-c-1 bundle projection, cp : X ~ W, with a nontrivial morphism, ~ : W ~ Y, with dimY < dlmW. In this case a general fibre of p is a nontrivial bundle and not a projective space. 1). 3). Any divisorial fiber F of p satisfies F'Z = 0 and hence F E p*Pic(Y), which is clearly not possible.

1) Kx^+tL^ is spanned under the above conditions with H very ample except for "obvious" exceptions. 5) is true if t > (n - ~:(Kx^+ tL^, X^))/2 + 1 and 0 < ~:(Kx^+ tL^, X ^) < n. Sommese, On the adjunction theoretic classification of projective varieties, Math. , 290 (1991), 31--62. Sommese, On the discriminant variety of a projective manifold, [BS1] [BS2] [E1] rE2] IF] [Ful] if:d] lll preprint. Sommese, New properties of special varieties arising from adjunction theory, to appear in J. Math. Soc.

Ein, Varieties with small dual varieties, II, Duke Math. , 52 (1985), 895-907. Fania, Configurations o f - 2 rational curves on sectional surfaces of n-folds, Math. , 275 (1986), 317-325. T. Fujita, On polarized manifolds whose adjoint bundles are not semipositive, Algebraic Geometry, Sendai, 1985, Advanced Studies in Pure Math. 10 (1987), 167-178. Fujita, On adjoint bundles of ample vector bundles, preprint. Ionescu, Generalized adjunction and applications, Math. Proc. Cambridge, Phil. , 99 (1986), 457-472.