{"paper":{"title":"On the Galois groups of the dualizing coverings for plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Vik.S. Kulikov","submitted_at":"2014-03-06T12:05:09Z","abstract_excerpt":"Let $C_1$ be an irreducible component of a reduced projective curve $C\\subset \\mathbb P^2$ defined over the field $\\mathbb C$, $\\mathrm{deg} C_1\\geq 2$, and let $T$ be the set of lines $l\\subset \\mathbb P^2$ meeting $C$ transversally. In the article, we prove that for a line $l_0\\in T$ and any two points $P_1,P_2\\in C_1\\cap l_0$ there is a loop $l_t\\subset T$, $t\\in [0,1]$, such that the movement of the line $l_0$ along the loop $l_t$ induces the transposition of the points $P_1$, $P_2$ and the identity permutation of the other points of $C\\cap l_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1426","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"}