A primer on toric varieties (Q2087696)

Toric varieties are particular algebraic varieties which have a combinatorial flavour, as they are related to objects in discrete geometry, such as cones and polytopes. Therefore, toric varieties lie at the intersection of algebraic geometry, symplectic geometry, discrete geometry and combinatorics. The paper under review is a nicely written short survey about the theory of toric varieties. The author quickly guides the reader through the basic definitions in toric geometry and through some examples with pictures. In particular, she focuses on the three possible ways to construct toric varieties: ``from cones or fans (Sect. 2), from polytopes (Sect. 3) and as GIT quotients (Sect. 4)''.