SU(n)-structures through quotient by torus actions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914229496315904 |
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| author | Peres, Quentin |
| author_facet | Peres, Quentin |
| contents | We show that if $(X,g,J,ω)$ is a Kähler manifold with an $SU(n+s)$-structure and a Hamiltonian holomorphic action of a compact torus $T^s$, then the usual symplectic quotient $Y$ inherits an $SU(n)$-structure provided the existence of special $1$-forms on $X$, called twist forms. We then give several applications of our results: on complex projective spaces, on cones over Fano Kähler-Einstein manifold and on toric $\mathbb{C}\mathbb{P}^1$ bundles. We also study the geometry behind these structures in the case of $n=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05257 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SU(n)-structures through quotient by torus actions Peres, Quentin Differential Geometry We show that if $(X,g,J,ω)$ is a Kähler manifold with an $SU(n+s)$-structure and a Hamiltonian holomorphic action of a compact torus $T^s$, then the usual symplectic quotient $Y$ inherits an $SU(n)$-structure provided the existence of special $1$-forms on $X$, called twist forms. We then give several applications of our results: on complex projective spaces, on cones over Fano Kähler-Einstein manifold and on toric $\mathbb{C}\mathbb{P}^1$ bundles. We also study the geometry behind these structures in the case of $n=3$. |
| title | SU(n)-structures through quotient by torus actions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.05257 |