{"paper":{"title":"Inductive Solution of the Tangential Center Problem on Zero-Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Amelia \\'Alvarez S\\'anchez, Jos\\'e Luis Bravo Trinidad, Pavao Mardesi\\'c","submitted_at":"2012-02-27T11:33:05Z","abstract_excerpt":"Given a polynomial $f\\in\\C[z]$ of degree $m$, let $z_1(t),...,z_m(t)$ denote all algebraic functions defined by $f(z_k(t))=t$. Given integers $n_1...,n_m$ such that $n_1+...+n_m=0$, the tangential center problem on zero-cycles asks to find all polynomials $g\\in\\C[z]$ such that $n_1g(z_1(t))+...+n_mg(z_m(t))\\equiv 0$. The classical Center-Focus Problem, or rather its tangential version in important non-trivial planar systems lead to the above problem.\n  The tangential center problem on zero-cycles was recently solved in a preprint by Gavrilov and Pakovich.\n  Here we give an alternative solution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5896","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"}