{"paper":{"title":"Associated forms of binary quartics and ternary cubics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV"],"primary_cat":"math.AG","authors_text":"A. V. Isaev, J. Alper, N. G. Kruzhilin","submitted_at":"2014-09-30T02:55:40Z","abstract_excerpt":"Let ${\\mathcal Q}_n^d$ be the vector space of forms of degree $d\\ge 3$ on ${\\mathbb C}^n$, with $n\\ge 2$. The object of our study is the map $\\Phi$, introduced in papers [EI], [AI1], that assigns every nondegenerate form in ${\\mathcal Q}_n^d$ the so-called associated form, which is an element of ${\\mathcal Q}_n^{n(d-2)*}$. We focus on two cases: those of binary quartics ($n=2$, $d=4$) and ternary cubics ($n=3$, $d=3$). In these situations the map $\\Phi$ induces a rational equivariant involution on the projectivized space ${\\mathbb P}({\\mathcal Q}_n^d)$, which is in fact the only nontrivial rat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8369","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"}