{"paper":{"title":"On a class of spaces of skew-symmetric forms related to Hamiltonian systems of conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"E Ferapontov, L Manivel","submitted_at":"2018-10-29T16:08:54Z","abstract_excerpt":"It was shown in \\cite{FPV} that the  classification of $n$-component systems of conservation laws possessing a third-order Hamiltonian structure reduces to the following algebraic problem: classify $n$-planes $H$ in $\\wedge^2(V_{n+2})$ such that  the induced map $Sym^2H\\longrightarrow  \\wedge^4V_{n+2}$ has 1-dimensional kernel  generated by a non-degenerate quadratic form on $H^*$. This problem is trivial for $n=2, 3$ and apparently wild for $n\\geq 5$. In this paper we address the most interesting borderline case $n=4$.  We prove that the variety $\\mathcal{V}$ parametrizing those 4-planes $H$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12216","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"}