{"paper":{"title":"Varieties of general type with the same Betti numbers as $\\mathbb P^1\\times \\mathbb P^1\\times\\ldots\\times \\mathbb P^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Amir D\\v{z}ambi\\'c","submitted_at":"2014-11-12T22:39:18Z","abstract_excerpt":"We study quotients $\\Gamma\\backslash \\mathbb H^n$ of the $n$-fold product of the upper half plane $\\mathbb H$ by irreducible and torsion-free lattices $\\Gamma < PSL_2(\\mathbb R)^n$ with the same Betti numbers as the $n$-fold product $(\\mathbb P^1)^n$ of projective lines. Such varieties are called fake products of projective lines or fake $(\\mathbb P^1)^n$. These are higher dimensional analogs of fake quadrics. In this paper we show that the number of fake $(\\mathbb P^1)^n$ is finite (independently of $n$), we give examples of fake $(\\mathbb P^1)^4$ and show that for $n>4$ there are no fake $(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3384","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"}