Abstract:
The aim of the present thesis is to study, develop and implement certain algorithms
in order to find the type of singularities for isolated complete intersection singularities
w.r.t contact equivalence of modality ≤ 1 defined over an algebraically closed field
K. The new investigation is that we do not compute the normal form of a given
singularity because this would be space and time consuming. We present a charac-
terization of the different types of singularities in terms of certain invariants and use
the characterization to identify the singularities. We describe our implementation in
computer algebra system Singular. Therefore, we discuss three problems in this
thesis.
• Problem 1 deals with the classification of hypersurface singularities with respect
to contact equivalence when the characteristic of the field p > 2 by using blowing
up as a new tool.
• Problem 2 studies the classification of simple complete intersection singularities
in terms of certain invariants when the characteristic of the field p = 0.
• Problem 3 includes to find the complete list of unimodular complete intersection
space curve singularities and the characterization of these singularities in terms
of certain invariants when the characteristic of the field p = 0
