Journal article

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

Harm Derksen, Visu Makam

ADVANCES IN MATHEMATICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2020

Abstract

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.

University of Melbourne Researchers

Grants

Awarded by National Science Foundation


Awarded by NSF


Funding Acknowledgements

The first author was supported by the National Science Foundation under Grant No. DMS-1601229. The second author was supported by NSF Grant No. DMS-1601229, DMS-1638352, and CCF-1412958.