{"paper":{"title":"The Essential Skeleton of a product of degenerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Enrica Mazzon, Morgan Brown","submitted_at":"2017-12-19T21:55:58Z","abstract_excerpt":"We study the problem of how the dual complex of the special fiber of an snc degeneration $\\cX_R$ changes under products. We view the dual complex as a skeleton inside the Berkovich space associated to $X_K$. Using the Kato fan, we define a skeleton $\\Sk(\\cX_R)$ when the model $\\cX_R$ is log-regular. We show that if $\\cX_R$ and $\\cY_R$ are log-regular, and at least one is semistable, then $\\Sk(\\cX_R\\times_R \\cY_R) \\simeq \\Sk(\\cX_R)\\times \\Sk(\\cY_R)$.\n  The essential skeleton $\\Sk(X_K)$, defined by Musta\\c{t}\\u{a} and Nicaise, is a birational invariant of $X_K$ and is independent of the choice o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07235","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"}