The universal deformation space of hypertoric variety and its applications
Takahiro Nagaoka (Kyoto)
Monday 17th September, 2018 16:00-17:00 Maths 311B
Hypertoric variety Y(A, alpha) is a (holomorphic) symplectic variety, which is defined as a Hamiltonian reduction of complex vector space by torus action. This is an analogue of toric variety. Actually, its geometric properties can be studied through the associated hyperplane arrangements (instead of polytopes). By definition, there exists a projective morphism pi:Y(A, alpha) to Y(A, 0), and for generic alpha, this gives a symplectic resolution of an affine hypertoric variety Y(A, 0). In general, for a (conical) symplectic variety and its symplectic resolution, Namikawa showed the existence of the universal Poisson deformation space of them. We construct the universal Poisson deformation space of hypertoric varieties Y(A, alpha) and Y(A, 0). We will explain this construction. In application, we can classify affine hypertoric varieties by the associated matroids. If time permits, we will also talk about applications to counting resolutions of affine hypertoric varieties. This talk is based on my master thesis.