no. 4
Constructive invariant theory for tori
Annales de l'Institut Fourier, Tome 43 (1993) no. 4, pp. 1055-1066.

Considérons une représentation rationnelle d’un tore algébrique T sur un espace vectoriel V. Soit {f 1 ,⋯,f p } un ensemble générateur homogène minimal pour l’anneau des invariants k[V] T . De nouvelles bornes supérieures sont établies pour le nombre N V,T := max { deg f i }. Ces bornes sont exprimées en termes du volume de l’enveloppe convexe des poids de V et d’autres données géométriques. De plus on décrit un algorithme pour construire un ensemble partiel (essentiellement unique) {f 1 ,⋯,f s } dont les éléments sont des monômes et tel que k[V] T soit intègre sur k[f 1 ,⋯,f s ].

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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     author = {Wehlau, David},
     title = {Constructive invariant theory for tori},
     journal = {Annales de l'Institut Fourier},
     pages = {1055--1066},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {4},
     year = {1993},
     doi = {10.5802/aif.1364},
     zbl = {0789.14009},
     mrnumber = {95c:14068},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1364/}
}
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Wehlau, David. Constructive invariant theory for tori. Annales de l'Institut Fourier, Tome 43 (1993) no. 4, pp. 1055-1066. doi : 10.5802/aif.1364. https://aif.centre-mersenne.org/articles/10.5802/aif.1364/

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