{"paper":{"title":"Numerical invariants of Fano 4-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"C. Casagrande","submitted_at":"2012-01-26T09:18:57Z","abstract_excerpt":"Let X be a (smooth, complex) Fano 4-fold. For any prime divisor D in X, consider the image of N_1(D) in N_1(X) under the push-forward of 1-cycles, and let c_D be its codimension in N_1(X). We define an integral invariant c_X of X as the maximal c_D, where D varies among all prime divisors in X. One easily sees that c_X is at most rho_X-1 (where rho is the Picard number), and that c_X is greater or equal than rho_X-rho_D, for any prime divisor D in X. We know from previous works that if c_X > 2, then either X is a product of Del Pezzo surfaces and rho_X is at most 18, or c_X=3 and rho_X is at m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5464","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":""},"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"}