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For these surfaces, we compute the associated Kummer lattice $K_{G}$, which is the minimal primitive sub-lattice containing the exceptional curves of the resolution $X\\to T/G$.\n  We then prove that a K3 surface is a generalised Kummer surface of type $Km(T,G)$ if and only if its N\\'eron-Severi group contains $K_{G}$.\n  For smooth-or"},"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":"1708.09358","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-30T16:47:47Z","cross_cats_sorted":[],"title_canon_sha256":"f1aa69ec9be23375941e47add0ebf52c8ae0f34683cc4d71941cff36eff30f84","abstract_canon_sha256":"ed2d7ab95898d812cfa063eb2c6103caf098c72d16d858b40f2b904c382cd303"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:04.502871Z","signature_b64":"WJj8mH1o722G5XrUzuMK5PBIXtyDIrxnL8dtp4FJnkZ/36SDmWCfXVCZUQ/6pm3IuCUfuFCLDmDaBs3Erp6YDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8558ad487b9fe8407c552aa21ad9c05f3ce13b44481829fd036be30ee09167c","last_reissued_at":"2026-05-18T00:27:04.502342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:04.502342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On generalized Kummer surfaces and the orbifold Bogomolov-Miyaoka-Yau inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Xavier Roulleau","submitted_at":"2017-08-30T16:47:47Z","abstract_excerpt":"A generalized Kummer surface $X=Km(T,G)$ is the resolution of a quotient of a torus $T$ by a finite group of symplectic automorphisms $G$. 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