{"paper":{"title":"A matroid invariant via the K-theory of the Grassmannian","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"David E Speyer","submitted_at":"2006-03-23T15:42:15Z","abstract_excerpt":"Let G(d,n) denote the Grassmannian of d-planes in C^n and let T be the torus (C^*)^n/diag(C^*) which acts on G(d,n). Let x be a point of G(d,n) and let \\bar{Tx} be the closure of the T-orbit through x. Then the class of the structure sheaf of \\bar{Tx} in the K-theory of G(d,n) depends only on which Pl\\\"ucker coordinates of x are nonzero -- combinatorial data known as the matroid of x. In this paper, we will define a certain map of additive groups from the K-theory of G(d,n) to Z[t]. Letting g_x(t) denote the image of (-1)^{n-dim Tx} [ O_{\\bar{Tx}}], g_x behaves nicely under the standard constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0603551","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0603551/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}