{"paper":{"title":"Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The moduli stack of stable L-valued G-Higgs bundles is Deligne-Mumford when G is semisimple.","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Sang-Bum Yoo, Sanghyeon Lee","submitted_at":"2026-05-13T15:15:29Z","abstract_excerpt":"For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact K\\\"ahler manifold $X$, extending known results for $\\Omega_X^{1}$-valued $G$-Higgs bundles.\n  Using this computation, when $G$ is semisimple and $X$ is a smooth projective variety, we show that the moduli stack of stable $L$-valued $G$-Higgs bundles is a Deligne-Mumford (DM) stack.\n  Furthermore, when $X$ is a smooth projective surface and $L=K_X$, we construct a symmetric perfect obstruction theory on this stable locus. We expect this will provide a foundat"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"when G is semisimple and X is a smooth projective variety, we show that the moduli stack of stable L-valued G-Higgs bundles is a Deligne-Mumford (DM) stack. Furthermore, when X is a smooth projective surface and L=K_X, we construct a symmetric perfect obstruction theory on this stable locus.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The computation of infinitesimal automorphisms for arbitrary L-valued bundles extends without additional restrictions from the known Ω¹_X case, and the stability condition is compatible with the stack structure in the required way; these steps are invoked but not detailed in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Infinitesimal automorphisms of L-valued G-Higgs bundles are computed, proving the stable moduli stack is Deligne-Mumford for semisimple G and yielding a symmetric perfect obstruction theory on surfaces when L = K_X.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The moduli stack of stable L-valued G-Higgs bundles is Deligne-Mumford when G is semisimple.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"19ec7e04ab3eacf7d764c636b59c3ad49cd3d69cf1a67f1bc05ccaa83ebfbec7"},"source":{"id":"2605.13657","kind":"arxiv","version":1},"verdict":{"id":"b8cf422e-e90f-4045-9f88-1bedefb8e1ae","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:49:19.381209Z","strongest_claim":"when G is semisimple and X is a smooth projective variety, we show that the moduli stack of stable L-valued G-Higgs bundles is a Deligne-Mumford (DM) stack. Furthermore, when X is a smooth projective surface and L=K_X, we construct a symmetric perfect obstruction theory on this stable locus.","one_line_summary":"Infinitesimal automorphisms of L-valued G-Higgs bundles are computed, proving the stable moduli stack is Deligne-Mumford for semisimple G and yielding a symmetric perfect obstruction theory on surfaces when L = K_X.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The computation of infinitesimal automorphisms for arbitrary L-valued bundles extends without additional restrictions from the known Ω¹_X case, and the stability condition is compatible with the stack structure in the required way; these steps are invoked but not detailed in the abstract.","pith_extraction_headline":"The moduli stack of stable L-valued G-Higgs bundles is Deligne-Mumford when G is semisimple."},"references":{"count":22,"sample":[{"doi":"","year":2026,"title":"Alper,Stacks and Moduli, 2026","work_id":"e1b6e4b6-9e66-47d4-b653-325c901a9894","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"´Alvarez-C´ onsul and O","work_id":"c454e293-c2ad-432f-9be7-1f616c51e8c7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2001,"title":"Hitchin-Kobayashi correspondence, quivers, and vortices","work_id":"a118683c-eb44-4518-a236-484d817a4b90","ref_index":3,"cited_arxiv_id":"math/0112161","is_internal_anchor":true},{"doi":"","year":2001,"title":"B. Anchouche, I. Biswas,Einstein-Hermitian connections on polystable principal bundles over a compact K¨ ahler manifold, American Journal of Mathematics.123(2)(2001), 207–228","work_id":"b829b207-09d9-4e09-8df9-904d1012dec6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"I. Biswas and G. Schumacher,Yang-Mills equation for stable Higgs sheaves, Int. J. Math.20(2009), 541–556","work_id":"f1999491-e8d9-423e-a09a-16eca618bf1b","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":22,"snapshot_sha256":"b735c585a014ecea713c9761bfa9547d193eca93990eb833e6aea4fa78fd01a2","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}