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We determine the following automorphism groups of $\\mathcal{M}_{n,d}$: (i) the group of automorphisms as a complex analytic variety, (ii) the group of holomorphic symplectomorphisms, (iii) the group of K\\\"ahler isomorphisms, (iv) the group of automorphisms of the quaternionic structure, (v) the group of hyper-K\\\"ahler isomorphisms. When $n$ and $d$ are coprime we show that $\\mathcal{M}_{n,d}$ admits an anti-holomorphic is"},"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":"1411.2228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-09T12:56:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"75b6aaf2d44978369481f475512d88af55a28ed31d170e20f17e03c468dd4ce7","abstract_canon_sha256":"ec4574a4fa0b8396b219535a3b2dde0b13aa80f4aed70b17281ccb279d5830ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:18.292071Z","signature_b64":"0y4M+0x1lno1nrKU13R05ID1alBG76e3PAHPbehyrl1NR549uzLs8F4rO922oC647DmVKhAejjKqU3a6iipBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9f9cb642d4b32703a677404e480b94cc93fd8a9cf06f79f7b4d7e69411239c0","last_reissued_at":"2026-05-18T01:14:18.291516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:18.291516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of the automorphism and isometry groups of Higgs bundle moduli spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"David Baraglia","submitted_at":"2014-11-09T12:56:22Z","abstract_excerpt":"Let $\\mathcal{M}_{n,d}$ be the moduli space of semi-stable rank $n$, trace-free Higgs bundles with fixed determinant of degree $d$ on a Riemann surface of genus at least $3$. 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