{"paper":{"title":"A Positivstellensatz for projective real varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claus Scheiderer","submitted_at":"2011-04-10T14:49:00Z","abstract_excerpt":"Given two positive definite forms f, g in R[x_0,...,x_n], we prove that fg^N is a sum of squares of forms for all sufficiently large N >= 0. We generalize this result to projective R-varieties X as follows. Suppose that X is reduced without one-dimensional irreducible components, and X(R) is Zariski dense in X. Given everywhere positive global sections f of L^{\\otimes2} and g of M^{\\otimes2}, where L, M are invertible sheaves on X and M is ample, fg^N is a sum of squares of sections of L\\otimes M^{\\otimes N} for all large N >= 0. In fact we prove a much more general version with semi-algebraic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1772","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"}