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We prove that the fixed locus of f consists of 28 isolated points and 1 K3 surface, moreover the anti-invariant lattice of the induced involution on H^2(X,Z) is isomorphic to E_8(-2). Finally we prove that any couple consisting of one such variety and a symplectic involution on it can be deformed into a couple consisting of the Hilbert square of a K3 surface and the involution induced by a Nikulin involution on the K3 surface."},"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":"1107.2854","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-14T15:40:14Z","cross_cats_sorted":[],"title_canon_sha256":"2e89b3f6ff177ac1387aa93e459eeb78c26430c28b2792f34ad5bb406cddfd7e","abstract_canon_sha256":"14431a71726dc2161269e343dfea18a6947572345b35f0d4291c07036d6c7662"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:12.336809Z","signature_b64":"1wnasMUxLQckK6Z/XfeD7SBv+aZwi0qWgYYfDChLXV6m4aFbpTJUziu6lZfatPV2w/W/E76F4L1KdIohX70RCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"021596a57fedf226f5d72e45892df941835777f1c0b6876f7dc4a99f4c61688b","last_reissued_at":"2026-05-18T03:55:12.336233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:12.336233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic involutions on deformations of K3^[2]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Giovanni Mongardi","submitted_at":"2011-07-14T15:40:14Z","abstract_excerpt":"Let X be a Hyperk\\\"{a}hler variety deformation equivalent to the Hilbert square on a K3 surface and let f be an involution preserving the symplectic form. 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