On the multiplication map of a multigraded algebra
  Given a multigraded algebra $A$, it is a natural question whether or not for two homogeneous components $A_u$ and $A_v$, the product $A_{nu}A_{nv}$ is the whole component $A_{nu+nv}$ for $n$ big enough. We give combinatorial and geometric answers to this question. 
Ivan V. Arzhantsev and Juergen Hausen