Toric Geometry originated from investigations of torus actions on geometric and algebraic objects. It is addressed through algebraic geometry, symplectic geometry, equivariant topology, as well as the theory of convex polyhedra within discrete mathematics. In spite of using their own language these completely diﬀerent disciplines often observe similar or even identical combinatorial phenomena. Thus toric geometry leads to a fascinating and fruitful interplay between these disciplines.
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Victor V. Batyrev, Klaus Altmann, Yael Karshon, Toric Geometry. Oberwolfach Rep. 6 (2009), no. 1, pp. 5–74DOI 10.4171/OWR/2009/01