50 research outputs found
Superisolated Surface Singularities
In this survey, we review part of the theory of superisolated surface
singularities (SIS) and its applications including some new and recent
developments. The class of SIS singularities is, in some sense, the simplest
class of germs of normal surface singularities. Namely, their tangent cones are
reduced curves and the geometry and topology of the SIS singularities can be
deduced from them. Thus this class \emph{contains}, in a canonical way, all the
complex projective plane curve theory, which gives a series of nice examples
and counterexamples. They were introduced by I. Luengo to show the
non-smoothness of the -constant stratum and have been used to answer
negatively some other interesting open questions. We review them and the new
results on normal surface singularities whose link are rational homology
spheres. We also discuss some positive results which have been proved for SIS
singularities.Comment: Survey article for the Proceedings of the Conference "Singularities
and Computer Algebra" on Occasion of Gert-Martin Greuel's 60th Birthday, LMS
Lecture Notes (to appear
On piecewise isomorphism of some varieties
Two quasi-projective varieties are called piecewise isomorphic if they can be
stratified into pairwise isomorphic strata. We show that the m-th symmetric
power of the complex affine space is piecewise isomorphic to
and the m-th symmetric power of the infinite
dimensional complex projective space is piecewise isomorphic to the infinite
dimensional Grassmannian