{"paper":{"title":"On a ring of modular forms related to the Theta gradients map in genus 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessio Fiorentino","submitted_at":"2011-09-11T23:25:16Z","abstract_excerpt":"The level moduli space $A_g^{4,8}$ is mapped to the projective space by means of gradients of odd Theta functions, such a map turning out no to be injective in the genus 2 case. In this work a congruence subgroup $\\Gamma$ is located between $\\Gamma_2(4,8)$ and $\\Gamma_2(2,4)$ in such a way the map factors on the related level moduli space $A_{\\Gamma}$, the new map being injective on $A_{\\Gamma}$. Satake's compactification $\\text{Proj}A(\\Gamma)$ and the desingularization $\\text{Proj}S(\\Gamma)$ are also due to be investigated, since the map does not extend to the boundary of the compactification"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2362","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"}