{"paper":{"title":"Projective toric generators in the unitary cobordism ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Grigory Solomadin, Yury Ustinovskiy","submitted_at":"2016-02-08T01:40:25Z","abstract_excerpt":"By the classical result of Milnor and Novikov, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\\Omega^U_*\\simeq \\mathbb Z[a_1,a_2,\\dots]$, ${\\rm deg}(a_i)=2i$. In this paper we solve a well-known problem of constructing geometric representatives for $a_i$ among smooth projective toric varieties, $a_n=[X^{n}], \\dim_\\mathbb C X^{n}=n$. Our proof uses a family of equivariant modifications (birational isomorphisms) $B_k(X)\\to X$ of an arbitrary smooth complex manifold $X$ of (complex) dimension $n$ ($n\\geq 2$, $k=0,\\dots,n-2$). The key fact is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02448","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"}