{"paper":{"title":"An exponential lower bound for the degrees of invariants of cubic forms and tensor actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.AC","math.RA"],"primary_cat":"math.RT","authors_text":"Harm Derksen, Visu Makam","submitted_at":"2019-02-27T20:35:31Z","abstract_excerpt":"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 ${\\rm SL}(V)$ on ${\\rm Sym}^3(V)^{\\oplus 4}$, the space of $4$-tuples of cubic forms, and the second is the action of ${\\rm SL}(V) \\times {\\rm SL}(W) \\times {\\rm SL}(Z)$ on the tensor space $(V \\otimes W \\otimes Z)^{\\oplus 9}$. In both these cases, we prove an exponential lower degree "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10773","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}