{"paper":{"title":"Virtual normalization and virtual fundamental classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alberto L\\'opez Mart\\'in","submitted_at":"2011-02-21T18:03:30Z","abstract_excerpt":"In this paper, we compare the virtual fundamental classes of the stacks of $(g,\\beta,\\mu)$-stable ramified maps $\\bar{\\mathfrak U}_{g,\\mu}(X,\\beta)$ and of $(g,\\beta,\\mu)$-log stable ramified maps $\\bar{\\mathfrak U}^{\\mathrm{log}}_{g,\\mu}(X,\\beta)$. For that we will see how they are identified via virtual normalization and then apply Costello's push-forward formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4294","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"}