TOPOLOGY OF 1-PARAMETER DEFORMATIONS OF NON-ISOLATED REAL SINGULARITIES

One-Parameter Toric Deformations of Cyclic Quotient Singularities

In the case of two-dimensional cyclic quotient singularities, we classify all oneparameter toric deformations in terms of certain Minkowski decompositions introduced by Altmann [1]. In particular, we describe to which components each such deformation maps, show how to induce each deformation from a versal family, give explicit equations for each deformation, describe the singularities in the ge...

Effective Methods to Compute the Topology of Real Algebraic Surfaces with Isolated Singularities

Given a real algebraic surface S in RP3, we propose a constructive procedure to determine the topology of S and to compute non-trivial topological invariants for the pair (RP3, S) under the hypothesis that the real singularities of S are isolated. In particular, starting from an implicit equation of the surface, we compute the number of connected components of S, their Euler characteristics and...

The topology of isolated singularities on complex hypersurfaces

Smoothings of Schemes with Non-isolated Singularities

In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally we obtain explicit criteria in order for a pure and reduced scheme of finite type over a field k to have smoothings and Q-Gorenstein smoothings.

The Vanishing Neighbourhood of Non-isolated Singularities

We study the vanishing neighbourhood of non-isolated singularities of functions on singular spaces by associating a general linear function. We use the carrousel monodromy in order to show how to get a better control over the attaching of thimbles. For one dimensional singularities, we prove obstructions to integer (co)homology groups and to the eigenspaces of the monodromy via monodromies of n...