{"paper":{"title":"Motivic Volumes of Fibers of Tropicalization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jeremy Usatine","submitted_at":"2018-05-22T03:09:19Z","abstract_excerpt":"Let $T$ be an algebraic torus over an algebraically closed field, let $X$ be a smooth closed subvariety of a $T$-toric variety such that $U = X \\cap T$ is not empty, and let $\\mathscr{L}(X)$ be the arc scheme of $X$. We define a tropicalization map on $\\mathscr{L}(X) \\setminus \\mathscr{L}(X \\setminus U)$, the set of arcs of $X$ that do not factor through $X \\setminus U$. We show that each fiber of this tropicalization map is a constructible subset of $\\mathscr{L}(X)$ and therefore has a motivic volume. We prove that if $U$ has a compactification with simple normal crossing boundary, then the g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08372","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"}