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Homogeneous polynomials with isomorphic Milnor algebras

Imran Ahmed (2010)

Czechoslovak Mathematical Journal

We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.

Hyperdéterminant d’un S L 2 -homomorphisme

Jean Vallès (2008)

Annales mathématiques Blaise Pascal

Etant donnés A 1 , , A s ( s 3 ) des S L 2 ( ) -modules non triviaux de dimensions respectives n 1 + 1 n s + 1 (avec n 1 = n 2 + + n s ) et φ ( A 2 A s , A 1 * ) un S L 2 ( ) -homomorphisme, nous montrons que l’hyperdéterminant de φ est nul sauf si les modules A i sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.

Immersions of module varieties

Grzegorz Zwara (1999)

Colloquium Mathematicae

We show that a homomorphism of algebras is a categorical epimorphism if and only if all induced morphisms of the associated module varieties are immersions. This enables us to classify all minimal singularities in the subvarieties of modules from homogeneous standard tubes.

Infinitesimal unipotent group schemes of complexity 1

Rolf Farnsteiner, Gerhard Röhrle, Detlef Voigt (2001)

Colloquium Mathematicae

We classify the uniserial infinitesimal unipotent commutative groups of finite representation type over algebraically closed fields. As an application we provide detailed information on the structure of those infinitesimal groups whose distribution algebras have a representation-finite principal block.

Introduction to actions of algebraic groups

Michel Brion (2010)

Les cours du CIRM

These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.

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