{"paper":{"title":"Logarithmic Quot spaces, boundedness, and K-tropicalizations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dhruv Ranganathan, Patrick Kennedy-Hunt","submitted_at":"2025-08-11T16:55:53Z","abstract_excerpt":"Logarithmic Hilbert and Quot spaces are generalizations of their traditional versions adapted to study pairs and degenerations. The logarithmic Quot spaces of $(X,D)$ parameterize \"algebraically transverse\" (logarithmically flat) quotient sheaves on degenerations of $X$. We prove boundedness and deduce properness of logarithmic Quot spaces. The results complete the basic foundations of logarithmic Quot spaces and specialize to work of Li-Wu and Maulik and the second author in special cases. Boundedness relies on two results of independent interest. First, we show that for a simple normal cross"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08175","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.08175/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}