$SU(n)$-structures through quotient by torus actions Article Swipe

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Quentin, Peres ·

YOU? · · 2025 · Open Access ·

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 $n = 3$.

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Mathematics

Holomorphic Function

Combinatorics

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Mathematics Quotient Torus Twist Pure mathematics Manifold (fluid mechanics) Symplectic geometry Holomorphic function Symplectic manifold Complex torus Symplectomorphism Complex manifold Action (physics) Toric variety Hamiltonian (control theory) Fano plane General position Clifford torus Combinatorics Maximal torus Differential geometry Projective geometry Algebra over a field

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Type: preprint
Language: en
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Title: $SU(n)$-structures through quotient by torus actions

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Language: en

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Publication year: 2025

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Publication date: 2025-11-18

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Authors: Quentin, Peres

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Concepts: Mathematics, Quotient, Torus, Twist, Pure mathematics, Manifold (fluid mechanics), Symplectic geometry, Holomorphic function, Symplectic manifold, Complex torus, Symplectomorphism, Complex manifold, Action (physics), Toric variety, Hamiltonian (control theory), Fano plane, General position, Clifford torus, Combinatorics, Maximal torus, Differential geometry, Projective geometry, Algebra over a field

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