{"paper":{"title":"Twisted Kodaira-Spencer classes and the geometry of surfaces of general type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Naie, Igor Reider","submitted_at":"2011-09-06T13:58:02Z","abstract_excerpt":"We study the cohomology groups $H^1(X,\\Theta_X(-mK_X))$, for $m\\geq1$, where $X$ is a smooth minimal complex surface of general type, $\\Theta_X$ its holomorphic tangent bundle, and $K_X$ its canonical divisor. One of the main results is a precise vanishing criterion for $H^1(X,\\Theta_X (-K_X))$.\n  The proof is based on the geometric interpretation of non-zero cohomology classes of $H^1(X,\\Theta_X (-K_X))$. This interpretation in turn uses higher rank vector bundles on $X$.\n  We apply our methods to the long standing conjecture saying that the irregularity of surfaces in $\\PP^4$ is at most 2. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1189","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"}