Muhammad Ahsan Binyamin, Junaid Alam Khan, Khawar Mehmood, Amir Shehzad, Umer Shuaib: Classification of right unimodal and bimodal hypersurface singularities in positive characteristic by invariants, 333-343

Abstract:

The complete classification of right unimodal and bimodal hypersurface singularities over a field of positive characteristic was given by H. D. Nguyen in form of a classifier, which allows the concrete classification from the given equation in a step by step procedure. The aim of this article is to characterize right unimodal and bimodal hypersurface singularities of corank $\leq 2$ by means of easy computable invariants such as the multiplicity, the Milnor number of the given equation and its blowing up. We also give a description of the algorithm to compute the type of right unimodal and bimodal hypersurface singularities without computing the normal form, which we have implemented in the computer algebra system SINGULAR.

Key Words: Right equivalence, Milnor number, Blowing up.

2010 Mathematics Subject Classification: Primary 14H20. Secondary 14Q05