3. A Characterization of non-singular toric varieties in terms of polyhedral cones (28.04.15).

Aim of the talk: Characterize morphisms between affine normal toric varieties and also the non-singularity of a normal affine toric variety in terms of their corresponding polyhedral cones.

Details: Explain [KKMSD73, I.1, Theorem 3]/[CLS11, Theorem 1.3.12] as well as [KKMSD73, I.1, Theorem 4]/[CLS11, Proposition 1.3.15] and their proofs. If time permits it would be nice to explain the $\dim =2$ case which is discussed on p.16-18, i.e., show that if $X$ is an affine normal toric variety of dimension 2, then it is non-singular iff it is isomorphic to ${\mathbb{A}}^2_k$ and in general it is a quotient of ${\mathbb{A}}^2_k$ by a finite cyclic group.

Jan