Algorithms for group actions in arbitrary characteristic and a problem in singularity theory

Abstract

We consider the actions of different groups G on the space M m,n of m ×

Isosingular loci of algebraic varieties

“…The second important assumption which holds only in characteristic 0 is that the orbit map associated to the (truncated) contact group K β is separable for all β large enough. In fact, the fact that this fails in positive characteristic was first exhibited by Greuel and Pham in [6,5] for certain isolated singularities. As we will see in Example 2.7, the results of Section 2 give new examples of this phenomenon, including the singularity f = x p + y p z mentioned above.…”

A note on finite determinacy of matrices

“…m = n = 1, as a key ingredient for classification of singularities (see [1,3]), and has been developed to matrices of power series recently in [4,5,8]. It was shown in [4,6] that in positive characteristic the tangent space to the orbit GA in general does not coincide with the image of the tangent map of the orbit map. For A ∈ M m,n instead of the tangent space we consider the R-submodule of M m,n…”