{"paper":{"title":"Smoothness and singularities of the perfect form and the second Voronoi compactification of ${\\mathcal A}_g$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.AG","authors_text":"Achill Sch\\\"urmann, Klaus Hulek, Mathieu Dutour Sikiri\\'c","submitted_at":"2013-03-23T13:34:03Z","abstract_excerpt":"We study the cones in the first Voronoi or perfect cone decomposition of quadratic forms with respect to the question which of these cones are basic or simplicial. As a consequence we deduce that the singular locus of the moduli stack ${\\mathcal A_g^{\\mathop{Perf}}}$, the toroidal compactification of the moduli space of principally polarized abelian varieties of dimension $g$ given by this decomposition, has codimension $10$ if $g \\geq 4$. Moreover we describe the non-simplicial locus in codimension $10$. We also show that the second Voronoi compactification ${\\mathcal A_{g}^{\\mathop{Vor}}}$ h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5846","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"}