Hypertoric variety $Y(A, \alpha)$ is a (holomorphic) symplectic variety, which is defined as Hamiltonian reduction of complex vector space by torus action. By definition, there exists projective morphism $\pi:Y(A, \alpha) \to Y(A, 0)$, and for generic $\alpha$, this gives a symplectic resolution of affine hypertoric variety $Y(A, 0)$.
In general, for conical symplectic variety and it's symplectic resolution, Namikawa showed the existence of universal Poisson deformation space of them.
We construct universal Poisson deformation space of hypertoric varieties $Y(A, \alpha)$, $Y(A, 0)$. We will explain this construction and concrete description of Namikawa-Weyl group action in this case. If time permits, We will also talk about some classification results of affine hypertoric variety. This talk is based on my master thesis.
The universal Poisson deformation space of hypertoric varieties.
Date
2018/02/23 Fri 16:30 - 18:00
Room
RIMS402号室
Speaker
Takahiro Nagaoka
Affiliation
Kyoto U.
Abstract