{"paper":{"title":"Spectral Curve of the Halphen Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrey E. Mironov, Dafeng Zuo","submitted_at":"2013-05-27T16:10:36Z","abstract_excerpt":"The Halphen operator is a third-order operator of the form $$\n  L_3=\\partial_x^3-g(g+2)\\wp(x)\\partial_x-\\frac{1}{2}g(g+2)\\wp'(x), $$ where $g\\ne 2\\,\\mbox{mod(3)}$, the Weierstrass $\\wp$-function satisfies the equation $$\n  (\\wp'(x))^2=4\\wp^3(x)-g_2\\wp(x)-g_3. $$ In the equianharmonic case, i.e., $g_2=0$ the Halphen operator commutes with some ordinary differential operator $L_n$ of order $n\\ne 0\\,\\mbox{mod(3)}.$ In this paper we find the spectral curve of the pair $L_3,L_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6267","kind":"arxiv","version":2},"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"}