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Constructive invariant theory for tori

David Wehlau (1993)

Annales de l'institut Fourier

Consider a rational representation of an algebraic torus T on a vector space V . Suppose that { f 1 , , f p } is a homogeneous minimal generating set for the ring of invariants, k [ V ] T . New upper bounds are derived for the number N V , T : = max { deg f i } . These bounds are expressed in terms of the volume of the convex hull of the weights of V and other geometric data. Also an algorithm is described for constructing an (essentially unique) partial set of generators { f 1 , , f s } consisting of monomials and such that k [ V ] T is integral over k [ f 1 , , f s ] .

Contractions of Lie algebras and algebraic groups

Dietrich Burde (2007)

Archivum Mathematicum

Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups.

Correspondencias divisoriales entre esquemas relativos.

Daniel Hernández Ruipérez (1981)

Revista Matemática Hispanoamericana

En este trabajo se estudian las correspondencias divisoriales entre dos esquemas relativos. Una correspondencia divisorial es una correspondencia algebraica entre los puntos de un esquema X y las clases de equivalencia lineal de divisores de otro esquema Y. Se consideran correspondencias triviales las que asignan a cada punto toda la variedad y las inversas de éstas. Por tanto las correspondencias divisoriales módulo las triviales son los divisores del producto módulo, módulo los divisores que provienen...

Courbes rationnelles sur les variétés homogènes

Nicolas Perrin (2002)

Annales de l’institut Fourier

Soit X une variété homogène sous un groupe G . Nous étudions les orbites maximales de X sous l’action d’un parabolique de G . Nous les décomposons en fibrations affines et projectives. Cette description permet de montrer que le schéma de Hilbert des courbes rationnelles lisses de classe fixée est non vide et irréductible.

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