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If there is a semistable Higgs vector bundle $(E\\,,\\theta)$ on $X$ with $\\theta\\,\\not=\\,0$, then we show that $c_1(TX)=0$, any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat K\\\"ahler form \\cite{Ya}. Let $(E\\,,\\theta)$ be a polystable Higgs vector bundle on a compact Ricci--flat K\\\"ahler manifold $X$. Let $h$ be an Hermitian structure on $E$ satisfying the Yang--Mills--Higgs equation for $(E\\,,\\theta)$. We prove that $h$ also satisfies the Yang--Mills--Higgs equatio"},"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":"1412.7738","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-24T19:19:13Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"bf5f4d324568b9a9548e79e0334ec88800d668d1fab9af9695276fd7494cef7e","abstract_canon_sha256":"f2077081efd87ee75bc4c59189d0c1222eb45d806f83486ae9c1752f4429890b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:25.045587Z","signature_b64":"F1Y1EwqYsQ4tEnNvLXI72blhfYS4VvAjhbcpu9R9cVf+tahyC2hkfyZ8hT1Xkbikvx7gaaTdnLbzA93DdRfWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab4b5d32647b3b968f7a22f5ef9942ca946f82a2c2c99c4caba95641a928ccef","last_reissued_at":"2026-05-18T00:36:25.044825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:25.044825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Yang-Mills-Higgs connections on Calabi-Yau manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Alessio Lo Giudice, Beatriz Gra\\~na Otero, Indranil Biswas, Ugo Bruzzo","submitted_at":"2014-12-24T19:19:13Z","abstract_excerpt":"Let $X$ be a compact connected K\\\"ahler--Einstein manifold with $c_1(TX)\\, \\geq\\, 0$. If there is a semistable Higgs vector bundle $(E\\,,\\theta)$ on $X$ with $\\theta\\,\\not=\\,0$, then we show that $c_1(TX)=0$, any $X$ satisfying this condition is called a Calabi--Yau manifold, and it admits a Ricci--flat K\\\"ahler form \\cite{Ya}. Let $(E\\,,\\theta)$ be a polystable Higgs vector bundle on a compact Ricci--flat K\\\"ahler manifold $X$. Let $h$ be an Hermitian structure on $E$ satisfying the Yang--Mills--Higgs equation for $(E\\,,\\theta)$. 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