2. Affine toric varieties and semigroups (21.05.15).

Aim of the talk: Generalize the previous talk by dropping the normality requirement. What does this imply for the cone?

Details: Repeat an example of a normal affine variety from a cone and then remove points from the semigroup such that the semigroup property is preserved. Do an example where the resulting semigroup becomes infinitely generated. This motivates the notion of a saturated semigroup. Explain the example $M\subseteq 2M$ to motivate the notion of semigroups that generate $M$.

Give the examples [Cox, Ex 1.12, 1.13, 1.15]. State [KKMSD73, Theorem 2] (without proof). The contents should cover I,§1 Definitions 1 and 2, Proposition 1, Lemma 1 and Theorem 1 of [KKMSD73]. We want to use the notation of [CLS11] and here we need to cover 1.1, especially Thm 1.1.17.

Benjamin L