arXiv subjects

Quentin Peres

Publications and source records attributed to Quentin Peres.

2 recordsLinked to original sources

arXiv2026

SU(3)-structures on quotients of 3-Sasakian orbifolds

We show that if $(S,g,\xi_i,\eta_i,\Phi_i)$ is a quasi-regular $3$-Sasakian orbifold of dimension $7$, then its quotient $Z$ by one of the Reeb vector fields inherits an $SU(3)$-structure parametrized by two real parameters. We compute its torsion and show that it is an LT-structure. Moreover, for certain values of the parameters, we can provide a nearly K\"ahler structure on $Z$ appearing as a special case of our construction. We give several examples in the regular, quasi-regular and orbifold cases.

math.DG↗

arXiv2025

SU(n)-structures through quotient by torus actions

We show that if $(X,g,J,\omega)$ is a K\"ahler 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 K\"ahler-Einstein manifold and on toric $\mathbb{C}\mathbb{P}^1$ bundles. We also study the geometry behind these structures in the case of $n=3$.

math.DG↗