Combinatorial structure of exceptional sets in resolutions of singularities
Abstract
Description
The dual complex can be associated to any resolution of singularities whose exceptional set is a divisor with simple normal crossings. It generalizes to higher dimensions the notion of the dual graph of a resolution of surface singularity. The homotopy type of the dual complex does not depend on the choice of a resolution and thus can be considered as an invariant of singularity. In this preprint we show that the dual complex is homotopy trivial for resolutions of 3-dimensional terminal singularities and for resolutions of Brieskorn singularities. We also review our earlier results on resolutions of rational and hypersurface singularities.
18 pages; to appear as a preprint of the Max-Planck-Institut, Bonn
18 pages; to appear as a preprint of the Max-Planck-Institut, Bonn