Constructive invariant theory for tori (Q1318005)

Consider a rational representation of an algebraic torus \(T\) on a vector space \(V\). Suppose that \(\{f_ 1,\dots,f_ p\}\) is a homogeneous minimal generating set for the ring of invariants, \({\mathbf k}[V]^ T\). 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 \(\{f_ 1,\dots,f_ s\}\) consisting of monomials and such that \({\mathbf k} [V]^ T\) is integral over \(k[f_ 1,\dots,f_ s]\).