A hyperkahler manifold M has a family of induced complex structures indexed by a two-dimensional sphere S-2 congruent to CP1. The twistor space of M is a complex manifold Tw( M) together with a natural holomorphic projection Tw(M) -> CP1, whose fiber over each point of CP1 is a copy of M with the corresponding induced complex structure. We remove one point from this sphere (corresponding to one fiber in the twistor space), and for the case of M = R-4n, n epsilon N, equipped with the standard hyperkahler structure, we construct one quantization that replaces the family of Berezin-Toeplitz quantizations parametrized by S-2 - {pt}. We provide semiclassical asymptotics for this quantization.
展开▼
