On the connectedness of the automorphism group of an affine toric variety

We obtain a criterion for the automorphism group of an affine toric variety to be connected, stated in combinatorial terms and in terms of the divisor class group of the variety. We describe the component group of the automorphism group of a nondegenerate affine toric variety. In particular, we show that the number of connected components of the automorphism group is finite.
Bibliography: 12 titles.