{"paper":{"title":"Maps of Mori dream spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andreas Hochenegger, Elena Martinengo","submitted_at":"2016-05-22T13:33:57Z","abstract_excerpt":"Given a map $\\phi: X \\to Y$ of $\\mathbb Q$-factorial Mori dream spaces, one can ask whether this map is induced by a homogeneous homomorphism $R(Y) \\to R(X)$ of Cox rings. As soon as $Y$ is singular, such a homomorphism needs not to exist, as pulling back Weil divisors is not well-defined. In this article, we prove that there is a unique Cox lift $\\Phi: \\mathcal X \\to \\mathcal Y$ of Mori dream stacks coming from a homogeneous homomorphism $R(Y) = R(\\mathcal Y) \\to R(\\mathcal X)$, where $\\mathcal Y$ is a canonical stack to $Y$ and $\\mathcal X$ is obtained from $X$ by root constructions. Moreove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06789","kind":"arxiv","version":3},"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"}