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In this paper, we will show that a symplectic circle action on a compact non-K\\\"{a}hler symplectic Calabi-Yau manifold may have a fixed point. More precisely, we will show that the symplectic $S^1$-manifold constructed by D. McDuff \\cite{McD} has the vanishing first Chern class. This manifold has the Betti numbers $b_1 = 3$, $b_2 = 8$, and $b_3 = 12$. In particular, it does not admit a"},"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":"1304.0540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-04-02T06:13:51Z","cross_cats_sorted":[],"title_canon_sha256":"58c690e4035092c4c7df8e7a1606ca1300f2bae8ccea40f681e4501b3f82bc4e","abstract_canon_sha256":"8ebcde7e0c7fe236475aed67d8d3dee4592453f13563e020f6dcaa566363a229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:15.093462Z","signature_b64":"WAzuo7eUTUzAuAGkan3FWBSPHsKrgwoE4WAVtYVnQUTn0pdFv6FkKMP87Ri1H84hPZRxV3PNDqaCUiRuBIcuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"853c69e1ffd7ae0a366c74b09a168229e319333a33e2dd684cdbc0ad2cd98e80","last_reissued_at":"2026-05-18T03:29:15.092677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:15.092677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An example of circle actions on symplectic Calabi-Yau manifolds with non-empty fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Min Kyu Kim, Yunhyung Cho","submitted_at":"2013-04-02T06:13:51Z","abstract_excerpt":"Let $(X,\\sigma,J)$ be a compact K\\\"{a}hler Calabi-Yau manifold equipped with a symplectic circle action. 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