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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 ] .

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