ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14 Catanese, Fabrizio, G. A. Universität Göttingen Bidouble covers and surface geography A bidouble cover is an Abelian cover X - Y of degree four with group (Z/2)^{2}. Examples where X is smooth and Y is a smooth quadric lead in the 80’s to interesting insight into the moduli spaces of surfaces of general type , and to still open problems concerning their differentiable structures. Allowing the 3 branch divisors to meet, P. Burniat was able in the 60’s to construct some interesting surfaces of general type. One can also allow singularities , and build a general theory by which one can construct canonical surfaces into new areas of surface geography.