{"paper":{"title":"The Degree Complexity of Smooth Surfaces of codimension 2","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":"2010-08-05T14:06:33Z","abstract_excerpt":"D.Bayer and D.Mumford introduced the degree complexity of a projective scheme for the given term order as the maximal degree of the reduced Gr\\\"{o}bner basis. It is well-known that the degree complexity with respect to the graded reverse lexicographic order is equal to the Castelnuovo-Mumford regularity (\\cite{BS}). However, little is known about the degree complexity with respect to the graded lexicographic order (\\cite{A}, \\cite{CS}).\n  In this paper, we study the degree complexity of a smooth irreducible surface in $\\p^4$ with respect to the graded lexicographic order and its geometric mean"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0978","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"}