{"paper":{"title":"Perverse obstructions to flat regular compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Patrick Brosnan","submitted_at":"2016-12-05T02:00:24Z","abstract_excerpt":"Suppose $\\pi:W\\to S$ is a smooth, proper morphism over a variety $S$ contained as a Zariski open subset in a smooth, complex variety $\\bar S$. The goal of this note is to consider the question of when $\\pi$ admits a regular, flat compactification. In other words, when does there exists a flat, proper morphism $\\bar\\pi:\\overline{W}\\to\\bar S$ extending $\\pi$ with $\\overline{W}$ regular? One interesting recent example of this occurs in the preprint arXiv:1602.05534 of Laza, Sacca and Voisin where $\\pi$ is a family of abelian $5$-folds over a Zariski open subset $S$ of $\\bar S=\\mathbb{P}^5$. In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01220","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"}