{"paper":{"title":"Computing Quot schemes via marked bases over quasi-stable modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Cristina Bertone, Margherita Roggero, Mario Albert, Werner M. Seiler","submitted_at":"2015-11-11T16:00:38Z","abstract_excerpt":"Let $ \\Bbbk$ be a field of arbitrary characteristic, $A$ a Noetherian $ \\Bbbk$-algebra and consider the polynomial ring $A[\\mathbf x]=A[x_0,\\dots,x_n]$. We consider homogeneous submodules of $A[\\mathbf x]^m$ having a special set of generators: a marked basis over a quasi-stable module. Such a marked basis inherits several good properties of a Gr\\\"obner basis, including a Noetherian reduction relation. The set of submodules of $A[\\mathbf x]^m$ having a marked basis over a given quasi-stable module has an affine scheme structure that we are able to exhibit. Furthermore, the syzygies of a module "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03547","kind":"arxiv","version":3},"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"}