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Classically, the cone of effective curves on a $K3$ surface $S$ is generated by nonegative classes $C$, for which $(C,C)\\geq0$, and nodal classes $C$, for which $(C,C)=-2$; Hassett and Tschinkel conjecture that the cone of effective curves on a holomorphic symplectic variety $X$ is similarly controlled by \"nodal\" classes $C$ such that $(C,C)=-\\gamma$, for $(\\cdot,\\cdot)$ now the Beauville-Bogomolov form, "},"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":"1111.0047","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-31T21:52:58Z","cross_cats_sorted":[],"title_canon_sha256":"a47ccb039b59fa9c7fa05bf41509a76e03663c0fabad44556e35f0ac49529e62","abstract_canon_sha256":"91164832ce1565bebbe56dd43e225babb8fd7068a183d99c4035b708aa97406c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:06.775592Z","signature_b64":"blAb5wPR2VQa7MGyKUQW/9KY35yAbAmqAMzjra8+i1gxRRThgQhnyVRtKv8COy04g6rBFIBEukbukKBjNMYLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a7adcce4c053b537c0d4be2e60d53063ec866802c659bd1c39f6c0dc6da92d8","last_reissued_at":"2026-05-18T03:15:06.774620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:06.774620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrangian 4-planes in holomorphic symplectic varieties of K3^[4] type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrei Jorza, Benjamin Bakker","submitted_at":"2011-10-31T21:52:58Z","abstract_excerpt":"We classify the cohomology classes of Lagrangian 4-planes $\\P^4$ in a smooth manifold $X$ deformation equivalent to a Hilbert scheme of 4 points on a $K3$ surface, up to the monodromy action. 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