Семинар НУЛ АГП "Automorphisms of complex moment-angle manifolds"

The construction of complex moment-angle manifolds is analogous to the quotient construction of toric varieties by Batyrev and Cox and provides quite a wide class of compact non-Kähler complex manifolds. It includes, for example, Hopf manifolds given by diagonalizable operators, Calabi-Eckmann manifolds, and their deformations.

In this talk, the fan defining the moment-angle manifold Z is assumed to be rational and regular, in which case Z is the total space of a holomorphic principal bundle with structure group a compact torus F over the corresponding toric variety X. By studying this bundle, we connect biholomorphic automorphisms of Z with the well-known description of automorphisms of complete toric varieties, whence we obtain a full description of Aut(Z) and its identity component.