{"paper":{"title":"On motivic vanishing cycles of critical loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dominic Joyce, Sven Meinhardt, Vittoria Bussi","submitted_at":"2013-05-28T09:37:50Z","abstract_excerpt":"Let $U$ be a smooth scheme over an algebraically closed field $\\mathbb K$ of characteristic zero and $f:U\\to{\\mathbb A}^1$ a regular function, and write $X=$Crit$(f)$, as a closed subscheme of $U$. The motivic vanishing cycle $MF_{U,f}^\\phi$ is an element of the $\\hat\\mu$-equivariant motivic Grothendieck ring ${\\mathcal M}^{\\hat\\mu}_X$ defined by Denef and Loeser math.AG/0006050 and Looijenga math.AG/0006220, and used in Kontsevich and Soibelman's theory of motivic Donaldson-Thomas invariants, arXiv:0811.2435.\n  We prove three main results:\n  (a) $MF_{U,f}^\\phi$ depends only on the third-order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6428","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"}