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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2605.13657 |
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| _version_ | 1866911681099071488 |
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| author | Lee, Sanghyeon Yoo, Sang-Bum |
| author_facet | Lee, Sanghyeon Yoo, Sang-Bum |
| contents | For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact Kähler manifold $X$, extending known results for $Ω_X^{1}$-valued $G$-Higgs bundles.
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.
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 foundation for defining Vafa-Witten invariants for reductive groups $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13657 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles Lee, Sanghyeon Yoo, Sang-Bum Algebraic Geometry Differential Geometry 14N99, 53C07 For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact Kähler manifold $X$, extending known results for $Ω_X^{1}$-valued $G$-Higgs bundles. 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. 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 foundation for defining Vafa-Witten invariants for reductive groups $G$. |
| title | Infinitesimal automorphisms and obstruction theory on the moduli of $L$-valued $G$-Higgs bundles |
| topic | Algebraic Geometry Differential Geometry 14N99, 53C07 |
| url | https://arxiv.org/abs/2605.13657 |