{"paper":{"title":"Complex Intersections of Real Cycles in Real Algebraic Varieties and Generalized Arnold-Viro Inequalities","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AG","authors_text":"S. Finashin","submitted_at":"1999-02-03T21:50:37Z","abstract_excerpt":"Consider a real algebraic variety, $\\R X$, of dimension $d$. If its complexification, $\\C X$, is a rational homology manifold (at least in a neighborhood of $\\R X$), then the intersection form in $\\C X$ defines a bilinear form in $d$-homologies of $\\R X$.\n Analizing it, one can obtain an information about $\\R X$, as it was done by V.I.Arnold in the case of non-singular double planes and then generalized by O.Ya.Viro and V.M.Kharlamov to the nodal surfaces.\n I present an integration (based on the Euler characteristic) formula, which expresses this form in terms of a certain local inveriant of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9902022","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"}