{"paper":{"title":"On the Infinitesimal Torelli theorem for regular surfaces with very ample canonical divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Igor Reider","submitted_at":"2018-03-04T14:03:10Z","abstract_excerpt":"Let $X$ be a smooth compact complex surface subject to the following conditions:\n  (i) the canonical line bundle $\\mathcal{O}_X(K_X) $ is very ample,\n  (ii) the irregularity $q(X): = h^1(\\mathcal{O}_X) =0$,\n  (iii) $X$ contains no rational normal curves of degree $\\leq (p_g-1)$,\n  (iv) the multiplication map $m_2: Sym^2(H^0(\\mathcal{O}_X(K_X))) \\longrightarrow H^0 (\\mathcal{O}_X (2K_X))$ is surjective.\n  It is shown that the Infinitesimal Torelli holds for such $X$.\n  Our proof is based on the study of the cup-product\n  $$ H^1 (\\Theta_X) \\longrightarrow (\\mathcal{O}_X(K_X))^{\\ast} \\otimes H^1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01357","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"}