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This gives a hyperbolic Riemannian metric on the projectivisation of the positive cone in $H^{1,1}(M,Q)$, denoted by $H$. Torelli theorem implies that the Hodge monodromy group $\\Gamma$ acts on $H$ with finite covolume, giving a hyperbolic orbifold $X=H/\\Gamma$. We show that there are finitely many geodesic h"},"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":"1511.02403","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2015-11-07T21:00:21Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"7308756f9c1d479140840b0c2f9b104a187f9c1634d19afeeeca5541b2ffe7f1","abstract_canon_sha256":"c8b7df2d89aa9b8c1f52a2fcc3dafbc3cacee3c22b822c5bdb026fe410131bce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:53.616476Z","signature_b64":"ct5fqBJX38zbq3YXJMzZAzolqW0GUyLo+z7Nau78/7OrTLziAANLZ4ty7x+JX6BhScUSwSsYT/6+nbi4XvwNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38e4882e1a6293ddff2c0aac9ebf2a4185d2330dc2f04de36731d0477a192a55","last_reissued_at":"2026-05-18T01:00:53.615632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:53.615632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hyperbolic geometry of the ample cone of a hyperkahler manifold","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ekaterina Amerik, Misha Verbitsky","submitted_at":"2015-11-07T21:00:21Z","abstract_excerpt":"Let $M$ be a compact hyperkahler manifold with maximal holonomy (IHS). 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