An exponential lower bound for the degrees of invariants of cubic forms and tensor actions.

Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower bounds for the maximal degree of a set of invariants that define Hilbert's null cone. We consider two actions: The first is the action of SL (V) on S 3 (V) ⊕ 4 , the space of 4-tuples of cubic forms, and the second is the action of SL (V) × SL (W) × SL (Z) on the tensor space (V ⊗ W ⊗ Z) ⊕ 9. In both these cases, we prove an exponential lower degree bound for a system of invariants that generate the invariant ring or that define the null cone. [ABSTRACT FROM AUTHOR]