The Conference on Algebraic Geometry, held in Berlin 9-15 March 1988, was organised by the Sektion Mathematik of the Humboldt-Universitat. The organising committee consisted of H. Kurke, W. Kleinert, G. Pfister and M. Roczen. The Conference is one in a series organised by the Humboldt-Universitat at regular intervals of two or three years, with the purpose of providing a meeting place for mathematicians from eastern and western countries. The present volume contains elaborations of part of the lectures presented at the Conference and some articles on related subjects. All papers were subject to the regular refereeing procedure of Compositio Mathematica, and H. Kurke acted as a guest editor of this journal. The papers focus on actual themes in algebraic geometry and singularity theory, such as vector bundles, arithmetical algebraic geometry, intersection theory, moduli and Hodge theory. We are grateful to all those who, by their hospitality, their presence at the Con­ ference, their support or their written contributions, have made this Conference to a success. The editors Compositio Mathematica 76: viii, 1990.

2-Cocycles and Azumaya algebras under birational transformations of algebraic schemes.- Monads and cohomology modules of rank 2 vector bundles.- On the Milnor fibrations of weighted homogeneous polynomials.- Mixed Hodge structures on the intersection cohomology of links.- Effective bounds for semipositive sheaves and for the height of points on curves over complex function fields.- Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen.- Chow categories.- Complex analytic compactifications of ?3.- Analytic curves in power series rings.- A Siegel Modular 3-fold that is a Picard Modular 3-fold.- Linearizing some ?/2? actions on affine space.- Normal forms and moduli spaces of curve singularities with semigroup .- On Castelnuovo's regularity and Hilbert functions.- Indecomposable Cohen-Macaulay modules and irreducible maps.- Fano bundles of rank 2 on surfaces.