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In particular, when n>107, every modular variety defined by an arithmetic group for a rational quadratic form of signature (2,n) is of general type. We also obtain similar finiteness in n>8 for the stable orthogonal groups. As a byproduct we derive finiteness of lattices admitting reflective modular form of bounded vanishing order, which proves a conjecture of Gritsenko and Nikulin."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.03225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-12T04:07:10Z","cross_cats_sorted":["math.NT","math.RT"],"title_canon_sha256":"bdef66511ef684912717a743b207ab8653cbbc1a60fb5b6c0ea0750c8a2fc63e","abstract_canon_sha256":"822070c094948726149813fd256699e5558e0af082f868002a83c8404129bd14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:44.099825Z","signature_b64":"0aLFsPgGM6zmPKcj798v8vq8tQrzIh3AY82mCJBSRKaAZzS/83tp2HIpwH5NfgZ6HflnEqxo0rf5xF2q2zTZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6008b0f402d660bb9a3687efacd032321ea94088cca53343583025d7e2826098","last_reissued_at":"2026-05-18T00:11:44.099025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:44.099025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Kodaira dimension of orthogonal modular varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Shouhei Ma","submitted_at":"2017-01-12T04:07:10Z","abstract_excerpt":"We prove that up to scaling there are only finitely many integral lattices L of signature (2,n) with n>20 or n=17 such that the modular variety defined by the orthogonal group of L is not of general type. 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