{"paper":{"title":"Configurations of points on degenerate varieties and properness of moduli spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Barbara Fantechi, Dan Abramovich","submitted_at":"2014-06-09T13:09:19Z","abstract_excerpt":"Consider a smooth variety $X$ and a smooth divisor $D\\subset X$. Kim and Sato (arXiv:0806.3819) define a natural compactification of $(X\\setminus D)^n$, denoted $X_D^{[n]}$, which is a moduli space of stable configurations of $n$ points lying on expansions of $(X,D)$ in the sense of Jun Li (arXiv:math/0009097, arXiv:math/0110113).\n  The purpose of this note is to generalize Kim and Sato's construction to the case where $X$ is an algebraic stack; and to construct an analogous projective moduli space $W_\\pi^{[n]}$ for a degeneration $\\pi:W \\to B$. We construct $X^n_D$ and $W_\\pi^{[n]}$ and prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2166","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"}