{"paper":{"title":"The Tangent Space at a Special Symplectic Instanton Bundle on $P_{2n+1}$","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Giorgio Ottaviani, G\\\"unther Trautmann","submitted_at":"1994-02-07T18:53:00Z","abstract_excerpt":"Mathematical instanton bundles on $ P_3$ have their analogues in rank--$2n$ instanton bundles on odd dimensional projective spaces $ P_{2n+1}$. The families of special instanton bundles on these spaces generalize the special 'tHooft bundles on $ P_3$. We prove that for a special symplectic instanton bundle $ E$ on $ P_{2n+1}$ with $c_2=k$ $h^1End( E) = 4(3n-1) k + (2n-5)(2n-1)$. Therefore the dimension of the moduli space of instanton bundles grows linearly in $k$. The main difference with the well known case of $ P_3$ is that $h^2End( E)$ is nonzero, in fact we prove that it grows quadratical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9402005","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"}