This volume consists of articles presented as talks at the Algebraic Geometry Conference held in the State Pedagogical Institute of Yaroslavl'from August 10 to 14, 1992. These conferences in Yaroslavl' have become traditional in the former USSR, now in Russia, since January 1979, and are held at least every two years. The present conference, the eighth one, was the first in which several foreign mathematicians participated. From the Russian side, 36 specialists in algebraic geometry and related fields (invariant theory, topology of manifolds, theory of categories, mathematical physics etc. ) were present. As well modern directions in algebraic geometry, such as the theory of exceptional bundles and helices on algebraic varieties, moduli of vector bundles on algebraic surfaces with applications to Donaldson's theory, geometry of Hilbert schemes of points, twistor spaces and applications to string theory, as more traditional areas, such as birational geometry of manifolds, adjunction theory, Hodge theory, problems of rationality in the invariant theory, topology of complex algebraic varieties and others were represented in the lectures of the conference. In the following we will give a brief sketch of the contents of the volume. In the paper of W. L. Baily three problems of algebro-geometric nature are posed. They are connected with hermitian symmetric tube domains. In particular, the 27-dimensional tube domain 'Fe is treated, on which a certain real form of E7 acts, which contains a "nice" arithmetic subgroup r e, as observed earlier by W. Baily.
Inhaltsverzeichnis
Three Problems on an Exceptional Domain.- On the Dimension of the Adjoint Linear System for Quadric Fibrations.- On the Stability of ME.- On a Class of Del Pezzo Fiber Spaces.- The Decomposition, Inertia and Ramification Groups in Birational Geometry.- Helix Theory and Nonsymmetrical Bilinear Forms.- On the Unramified 2-covers of the Curves of Genus 3.- Spatial Polygons and Stable Configurations of Points in the Projective Line.- Rigid Sheaves on Surfaces.- The Alexander Polynomials of Algebraic Curves in C2.- On the Brauer Group of Real Algebraic Surfaces.- Symplectic Twistors and Geometric Quantization of Strings.- Compactifications of C4 of Index 3.- A Note on Cohomologies of Exceptional Bundles on a Quadric Surface.- Exceptional Vector Bundles on a Del Pezzo Surface.- Standard Bundles on a Hilbert Scheme of Points on a Surface.- Top Segre Class of a Standard Vector Bundle ?D4 on the Hilbert Scheme Hilb4S of a Surface S.- Almost Canonical Polynomials of Algebraic Surfaces.
