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 firs...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2020-07, Vol.368, p.107136, Article 107136
Main Authors: Derksen, Harm, Makam, Visu
Format: Article
Language:English
Subjects:
Exponential lower bounds
Grosshans principle
Invariant rings
Moment map
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Summary: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 S3(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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107136