{"paper":{"title":"Vanishing Vanishing Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David B. Massey","submitted_at":"2006-10-09T18:56:57Z","abstract_excerpt":"If $\\Adot$ is a bounded, constructible complex of sheaves on a complex analytic space $X$, and $f:X\\to\\C$ and $g:X\\to\\C$ are complex analytic functions, then the iterated vanishing cycles $\\phi_g[-1](\\phi_f[-1]\\Adot)$ are important for a number of reasons. We give a formula for the stalk cohomology $H^*(\\phi_g[-1]\\phi_f[-1]\\Adot)_x$ in terms of relative polar curves, algebra, and the normal Morse data and micro-support of $\\Adot$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610296","kind":"arxiv","version":3},"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"}