{"paper":{"title":"Combinatorial Models for the Variety of Complete Quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Mahir Bilen Can, Michael Joyce, Soumya Banerjee","submitted_at":"2016-10-09T17:17:30Z","abstract_excerpt":"We develop several combinatorial models that are useful in the study of the $SL_n$-variety $\\mathcal{X}$ of complete quadrics. Barred permutations parameterize the fixed points of the action of a maximal torus $T$ of $SL_n$, while $\\mu$-involutions parameterize the orbits of a Borel subgroup of $SL_n$. Using these combinatorial objects, we characterize the $T$-stable curves and surfaces on $\\mathcal{X}$, compute the $T$-equivariant $K$-theory of $\\mathcal{X}$, and describe a Bia{\\l}ynicki-Birula cell decomposition for $\\mathcal{X}$. Furthermore, we give a computational characterization of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02698","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"}