{"paper":{"title":"Generic Initial ideals of Singular Curves in Graded Lexicographic Order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jeaman Ahn, Sijong Kwak, YeongSeok Song","submitted_at":"2011-07-30T06:43:14Z","abstract_excerpt":"In this paper, we are interested in the generic initial ideals of \\textit{singular} projective curves with respect to the graded lexicographic order. Let $C$ be a \\textit{singular} irreducible projective curve of degree $d\\geq 5$ with the arithmetic genus $\\rho_a(C)$ in $\\p^r$ where $r\\ge 3$. If $M(I_C)$ is the regularity of the lexicographic generic initial ideal of $I_C$ in a polynomial ring $k[x_0,..., x_r]$ then we prove that $M(I_C)$ is $1+\\binom{d-1}{2}-\\rho_a(C)$ which is obtained from the monomial $$ x_{r-3} x_{r-1}\\,^{\\binom{d-1}{2}-\\rho_a(C)}, $$ provided that $\\dim\\Tan_p(C)=2$ for e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0045","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"}