{"paper":{"title":"Universal covering calabi-yau manifolds of the Hilbert schemes of n points of Enriques surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Taro Hayashi","submitted_at":"2015-02-08T09:48:53Z","abstract_excerpt":"Throughout this paper, we work over ${\\mathbb C}$, and $n$ is an integer such that $n\\geq 2$. For an Enriques surface $E$, let $E^{[n]}$ be the Hilbert scheme of $n$ points of $E$. By Oguiso and Schr\\\"oer, $E^{[n]}$ has a Calabi-Yau manifold $X$ as the universal covering space, $\\pi :X\\rightarrow E^{[n]}$ of degree $2$. The purpose of this paper is to investigate a relationship of the small deformation of $E^{[n]}$ and that of $X$ $({\\rm Theorem}\\ 1.1)$, the natural automorphism of $E^{[n]}$ $({\\rm Theorem}\\,1.2)$, and count the number of isomorphism classes of the Hilbert schemes of $n$ point"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02231","kind":"arxiv","version":5},"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"}