{"paper":{"title":"Syzygies of some GIT quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Krishna Hanumanthu, S. Senthamarai Kannan","submitted_at":"2013-09-16T10:45:04Z","abstract_excerpt":"Let $X$ be flat scheme over $\\mathbb{Z}$ such that its base change, $X_p$, to $\\bar{\\mathbb{F}}_p$ is Frobenius split for all primes $p$. Let $G$ be a reductive group scheme over $\\mathbb{Z}$ acting on $X$. In this paper, we prove a result on the $N_p$ property for line bundles on GIT quotients of $X_{\\mathbb{C}}$ for the action of $G_{\\mathbb{C}}$. We apply our result to the special cases of (1) an action of a finite group on the projective space and (2) the action of a maximal torus on the flag variety of type $A_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3893","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"}