{"paper":{"title":"Conjugacy classes of commuting nilpotents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Donghoon Hyeon, William Haboush","submitted_at":"2016-06-30T19:28:34Z","abstract_excerpt":"We consider the space $\\mathcal M_{q,n}$ of regular $q$-tuples of commuting nilpotent endomorphisms of $k^n$ modulo simultaneous conjugation. We show that $\\mathcal M_{q,n}$ admits a natural homogeneous space structure, and that it is an affine space bundle over $\\mathbb P^{q-1}$. A closer look at the homogeneous structure reveals that, over $\\mathbb C$ and with respect to the complex topology, $\\mathcal M_{q,n}$ is a smooth vector bundle over $\\mathbb P^{q-1}$. We prove that, in this case, $\\mathcal M_{q,n}$ is diffeomorphic to a direct sum of twisted tangent bundles. We also prove that $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09625","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"}