{"paper":{"title":"An algebraic formula for the index of a 1-form on a real quotient singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sabir M. Gusein-Zade, Wolfgang Ebeling","submitted_at":"2017-08-30T11:32:26Z","abstract_excerpt":"Let a finite abelian group $G$ act (linearly) on the space $\\mathbb{R}^n$ and thus on its complexification $\\mathbb{C}^n$. Let $W$ be the real part of the quotient $\\mathbb{C}^n/G$ (in general $W \\neq \\mathbb{R}^n/G$). We give an algebraic formula for the radial index of a 1-form on the real quotient $W$. It is shown that this index is equal to the signature of the restriction of the residue pairing to the $G$-invariant part $\\Omega^G_\\omega$ of $\\Omega_\\omega= \\Omega^n_{\\mathbb{R}^n,0}/\\omega \\wedge \\Omega^{n-1}_{\\mathbb{R}^n,0}$. For a $G$-invariant function $f$, one has the so-called quantu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09219","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"}