Pith Number

pith:TD7VTEKO

pith:2026:TD7VTEKOUSDSB55H6DO5JF2T7Z

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Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles

Sang-Bum Yoo, Sanghyeon Lee

The moduli stack of stable L-valued G-Higgs bundles is Deligne-Mumford when G is semisimple.

arxiv:2605.13657 v1 · 2026-05-13 · math.AG · math.DG

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

22 extracted · 22 resolved · 1 Pith anchors

[1] Alper,Stacks and Moduli, 2026 2026

[2] ´Alvarez-C´ onsul and O 2003

[3] Hitchin-Kobayashi correspondence, quivers, and vortices 2001 · arXiv:math/0112161

[4] 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 2001

[5] I. Biswas and G. Schumacher,Yang-Mills equation for stable Higgs sheaves, Int. J. Math.20(2009), 541–556 2009

Receipt and verification

First computed	2026-05-18T02:44:17.374302Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98ff59914ea48720f7a7f0ddd49753fe7b6bff7a841d2b28df1ed10f26e81090

Aliases

arxiv: 2605.13657 · arxiv_version: 2605.13657v1 · doi: 10.48550/arxiv.2605.13657 · pith_short_12: TD7VTEKOUSDS · pith_short_16: TD7VTEKOUSDSB55H · pith_short_8: TD7VTEKO

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TD7VTEKOUSDSB55H6DO5JF2T7Z \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 98ff59914ea48720f7a7f0ddd49753fe7b6bff7a841d2b28df1ed10f26e81090

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cfb3462b57fa2846b24dfcf8d6025096dd768ef7d16a5fff7df0526614fa41f4",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T15:15:29Z",
    "title_canon_sha256": "eb1e7a701f20c05a19da4d43c52fdcea6672fefabac1a7158e200c7a42ef9da0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13657",
    "kind": "arxiv",
    "version": 1
  }
}