{"paper":{"title":"Chern classes and Characteristic Cycles of Determinantal Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Xiping Zhang","submitted_at":"2016-05-17T21:58:08Z","abstract_excerpt":"Let $K$ be an algebraically closed field of characteristic $0$. For $m\\geq n$, we define $\\tau_{m,n,k}$ to be the set of $m\\times n$ matrices over $K$ with kernel dimension $\\geq k$. This is a projective subvariety of $\\bbP^{mn-1}$, and is called the (generic) determinantal variety. In most cases $\\tau_{m,n,k}$ is singular with singular locus $\\tau_{m,n,k+1}$. In this paper we give explicit formulas computing the Chern-Mather class ($c_M$) and the Chern-Schwartz-MacPherson class ($c_{SM}$) of $\\tau_{m,n,k}$, as classes in the projective space. We also obtain formulas for the conormal cycles an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05380","kind":"arxiv","version":4},"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"}