25 citations · 32 across the 5 of their papers we have counts for
6 papers
Additive relative invariants and the components of a linear free divisor
Brian Pike
A 'prehomogeneous vector space' is a rational representation of a connected complex linear algebraic group that has a Zariski open orbit . Mi…
Solvable Group Representations and Free Divisors whose Complements are 's
James Damon, Brian Pike
We apply previous results on the representations of solvable linear algebraic groups to construct a new class of free divisors whose complements are 's. These free divisor…
Lifting free divisors
Ragnar-Olaf Buchweitz, Brian Pike
Let be a morphism between smooth complex analytic spaces, and let define a free divisor on . We prove that if the deformation space of is a Cohe…
On Fitting ideals of logarithmic vector fields and Saito's criterion
Brian Pike
The germ of an analytic set in has an associated -module of `logarithmic vector fields', the ambient ge…
Solvable Groups, Free Divisors and Nonisolated Matrix Singularities II: Vanishing Topology
James Damon, Brian Pike
In this paper we use the results from the first part to compute the vanishing topology for matrix singularities based on certain spaces of matrices. We place the variety of singula…
Solvable Groups, Free Divisors and Nonisolated Matrix Singularities I: Towers of Free Divisors
James Damon, Brian Pike
We introduce a method for obtaining new classes of free divisors from representations of connected linear algebraic groups where , with having an open…