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Sep 30, 2010 at 23:06 vote accept James Davidoff
Sep 30, 2010 at 22:49 comment added JRG His condition that $S$ lies in a hyperplane is equivalent to the existence of a $\mathbb C^*$ action for which each monomial is of the same degree. The weights are given by the normal vector to $H$. For instance, in example 3, $(6,0,0).(1,2,3)=(1,1,1).(1,2,3)=\cdots=6$, so the exponents lie in the hyperplane $a + 2b + 3c = 6$.
Sep 30, 2010 at 22:16 history answered Remke Kloosterman CC BY-SA 2.5