{"paper":{"title":"The non-existence of stable Schottky forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G. Codogni, N. I. Shepherd-Barron","submitted_at":"2011-12-28T15:40:43Z","abstract_excerpt":"Let $A_g^S$ be the Satake compactification of the moduli space $A_g$ of principally polarized abelian $g$-folds and $M_g^S$ the closure of the image of the moduli space $M_g$ of genus $g$ curves in $A_g$ under the Jacobian morphism. Then $A_g^S$ lies in the boundary of $A_{g+m}^S$ for any $m$. We prove that $M_{g+m}^S$ and $A_g^S$ do not meet transversely in $A_{g+m}^S$, but rather that their intersection contains the $m$th order infinitesimal neighbourhood of $M_g^S$ in $A_g^S$. We deduce that there is no non-trivial stable Siegel modular form that vanishes on $M_g$ for every $g$. In particul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6137","kind":"arxiv","version":4},"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"}