Computing Versal Deformations

Leibniz algebra deformations of a Lie algebra

In this note we compute Leibniz algebra deformations of the 3-dimensional nilpotent Lie algebra n3 and compare it with its Lie deformations. It turns out that there are 3 extra Leibniz deformations. We also describe the versal Leibniz deformation of n3 with the versal base.

1 4 Ju n 20 06 n - dimensional global correspondences of Langlands over singular schemes ( II )

Belgium " This paper is dedicated to R. Thom who, by his enthusiasm, convinced me of the importance of the singularities and, by his patience , backed me up along my long research towards the blowups of the versal deformations , the geometries of these processes and the (strange) attractors tied up to these ". Abstract A rather complete phenomenology of the singularities is developed according ...

Versal Unfoldings of Equivariant Linear Hamiltonian Vector Fields

We prove an equivariant version of Galin’s theorem on versal deformations of infinitesimally symplectic matrices. Matrix families of codimension zero and one are classified, and the results are used to study the movement of eigenvalues in one parameter families.

Simultaneous versal deformations of endomorphisms

We study the set M of pairs (f, V ), defined by an endomorphism f of F and a ddimensional f–invariant subspace V . It is shown that this set is a smooth manifold that defines a vector bundle on the Grassmann manifold. We apply this study to derive conditions for the Lipschitz stability of invariant subspaces and determine versal deformations of the elements of M with respect to a natural equiva...

δm CONSTANT LOCUS OF VERSAL DEFORMATIONS OF NONDEGENERATE HYPERSURFACE SIMPLE K3 SINGULARITIES