{"paper":{"title":"On Cohomology of the Square of an Ideal Sheaf","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Jonathan Wahl","submitted_at":"1996-01-29T16:26:13Z","abstract_excerpt":"For a smooth subvariety $X\\subset\\Bbb P^N$, consider (analogously to projective normality) the vanishing condition $H^1(\\Bbb P^N,\\Cal I^2_X(k))=0$, $k\\ge3$.  This condition is shown to be satisfied for all sufficiently large embeddings of a given $X$, and for a Veronese embedding of $\\Bbb P^n$. For $C\\subset\\Bbb P^{g-1}$, the canonical embedding of a non-hyperelliptic curve, this condition guarantees the vanishing of some obstruction groups to deformations of the cone. Recall that the tangents to deformations are dual to the cokernel of the Gaussian-Wahl map.\n  \\proclaim{Theorem} Suppose the G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9601027","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"}