Constructive invariant theory for tori

Wehlau, David. "Constructive invariant theory for tori." Annales de l'institut Fourier 43.4 (1993): 1055-1066. <http://eudml.org/doc/75025>.

@article{Wehlau1993,
abstract = {Consider a rational representation of an algebraic torus $T$ on a vector space $V$. Suppose that $\lbrace f_ 1, \dots ,f_p\rbrace $ is a homogeneous minimal generating set for the ring of invariants, $\{\bf k\}[V]^T$. New upper bounds are derived for the number $N_\{V,T\}:=\{\rm max\} \lbrace \{\rm deg\} f_i\rbrace $. 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 $\lbrace f_1,\dots ,f_s\rbrace $ consisting of monomials and such that $\{\bf k\} [V]^T$ is integral over $k[f_1,\dots ,f_s]$.},
author = {Wehlau, David},
journal = {Annales de l'institut Fourier},
keywords = {torus invariants; torus representations; algebraic torus; ring of invariants},
language = {eng},
number = {4},
pages = {1055-1066},
publisher = {Association des Annales de l'Institut Fourier},
title = {Constructive invariant theory for tori},
url = {http://eudml.org/doc/75025},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Wehlau, David
TI - Constructive invariant theory for tori
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 4
SP - 1055
EP - 1066
AB - Consider a rational representation of an algebraic torus $T$ on a vector space $V$. Suppose that $\lbrace f_ 1, \dots ,f_p\rbrace $ is a homogeneous minimal generating set for the ring of invariants, ${\bf k}[V]^T$. New upper bounds are derived for the number $N_{V,T}:={\rm max} \lbrace {\rm deg} f_i\rbrace $. 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 $\lbrace f_1,\dots ,f_s\rbrace $ consisting of monomials and such that ${\bf k} [V]^T$ is integral over $k[f_1,\dots ,f_s]$.
LA - eng
KW - torus invariants; torus representations; algebraic torus; ring of invariants
UR - http://eudml.org/doc/75025
ER -